Indium Solubility in Α-Gallium and Gallium-Indium Eutectic Alloys Studied Using PAC

Technical Report 2 National Science Foundation Grant DMR 09-04096 Metals Program

Indium solubility in α-gallium and gallium-indium eutectic alloys studied using PAC

Xiangyu Yin

August 2011

Hyperfine Interactions Group Department of Physics and Astronomy Washington State University Pullman, Washington 99164 USA

Foreword

This report is the MS thesis of Xiangyu Yin, defended May 9, 2011. The research described herein was supported in part by the National Science Foundation under grant DMR 09-04096 (Metals Program).

Gary S. Collins mailto:[email protected] May 2011

INDIUM SOLUBILITY IN α-GALLIUM AND GALLIUM-INDIUM

EUTECTIC ALLOYS STUDIED USING PAC

XIANGYU YIN

A thesis submitted in partial fulfillment of the requirement for the degree of

MASTER OF SCIENCE IN PHYSICS

WASHINGTON STATE UNIVERSITY

Department of Physics and Astronomy

AUGUST 2011

ACKNOWLEDGEMENT

I would like to thank my advisor Professor Gary S. Collins for his patient guidance and assistant with my research.

I would also like to thank Randy Newhouse, John Bevington for their help and advice on my experiments. Discussion with Dr. Heinz Haas was also appreciated.

I would like to express my gratitude to my parents for their encouragement and support.

iii

INDIUM SOLUBILITY IN α-GALLIUM AND GALLIUM-INDIUM

EUTECTIC ALLOYS STUDIED USING PAC

Abstract

by Xiangyu Yin M.S. Washington State University August 2011

Chair: Gary S. Collins

The melting temperature of α-gallium is 303K. The method of perturbed angular correlation of gamma rays (PAC) was used to determine the solubility of 111In probe atoms present at of 10-10 mole fraction. Below 303K and above the eutectic temperature of the gallium-indium binary system, approximately 10% of probes were observed through measurements of nuclear quadrupole interactions to be dissolved in solid gallium. This makes the terminal solubility about 10-11. Below the eutectic temperature, where the only stable phases are gallium and indium metals, the remaining 90% of indium probes, previous being in the liquid phase, were observed to crystallize into tetragonal indium metal, forming crystals of radioactive 111In. In other experiments, about 1% of natural indium or other elements were added to the sample to see their effects on the eutectic reaction. It turns out that bismuth, cadmium and zinc precipitate independently of indium, while tin precipitates with indium.

Cadmium-indium alloy at indium-rich region was also studied. Transformation between αT and αK phases are observed. The effect of cadmium impurities on indium metal signal is observed to be small. Mercury-indium system at mercury-rich region was also studied as another example of studying the boundary of binary phase diagram using PAC technique. The terminal solubility of indium in solid mercury was found to be greater than the 10-8 mole fraction of 111In in the samples.

TABLE OF CONTENTS

ACKNOWLEDGEMENT ...... iii

ABSTRACT ...... iv

LIST OF TABLES ...... vii

LIST OF FIGURES ...... viii

Chapter 1: Introduction ...... 1

Chapter 2: Experimental Methods ...... 2

2.1 PAC ...... 2

2.1.1 Introduction to PAC ...... 2

2.2 Closed-cycle Helium Refrigerator ...... 5

2.2.1 Installation...... 5

2.2.2 Operation and Temperature Accuracy ...... 6

2.3 Sample Preparation ...... 7

2.3.1 Gallium with 111In ...... 7

2.3.2 Gallium with 111In and ~1 at.% of other elements ...... 8

2.3.3 In-Cd Alloys ...... 8

Chapter 3: Theory ...... 9

3.1 Crystal Structures of Ga, In and others ...... 9

3.1.1 Gallium ...... 9

3.1.3 Mercury, Tin and Cadmium ...... 11

3.2 Binary phase diagram of Ga-In system and the calculation of the solubility ..... 12

3.2.1 Binary phase diagram of Ga-In system ...... 12

3.2.2 Method for determination of the terminal solubility ...... 13

3.3 Eutectic alloy and eutectic reaction ...... 15

3.4 Crystal structures of indium alloyed with several percent of cadmium...... 17

Chapter 4: Experiments...... 20

4.1 Solubility of In in solid α-Ga ...... 20

4.1.1 The measurement of solubility ...... 20

4.1.2 A test to determine the amount of natural indium ...... 22

4.1.3 The effect by adding 0.7 at.% of natural In ...... 27

4.2 Coarsening of morphology of eutectic alloy ...... 27

4.2.1 System having only 111In ...... 27

4.2.2 System having natural In ...... 31

4.3 EFG in In-Cd alloys ...... 32

4.4 The effect on forming eutectic alloy by adding other natural impurities ...... 37

4.5 Hg-rich region of the Hg-In binary system ...... 41

Chapter 5: Summary ...... 45

APPENDICES………………………………………………………………………….. 46

A. Two mysteries in the literature solved ...... 46

B. Temperature dependence of quadrupole interaction frequency of α-Ga ...... 48

BIBLIOGRAPHY………………………………………………………………………51

LIST OF TABLES

Table 1. Temperature to melt the samples……………………………………………..8

Table 2. The identification of phases from PAC spectra………………………………12

Table 3. The change of c/a ratio in In-Cd alloy with respect to composition at 25℃…18

Table 4. Signal observed in Ga-X-In ternary system…………………………………..40

Table 5. Temperature dependence of quadrupole interaction frequency and symmetric parameter of α-Ga…………………………………………………………….48

vii

LIST OF FIGURES

Fig. 1. Decay of 111In to 111Cd……………………………………………………………2

Fig. 2. PAC electronics schematic………………………………………………………..4

Fig. 3. The Configuration of Close Cycle Helium Refrigerator System…………………6

Fig. 4. Pressure-temperature phase diagram of Ga……………………………………….9

Fig. 5. Crystal Structure of α-Ga………………………………………………………..10

Fig. 6. Crystal Structure of In…………………………………………………………... 11

Fig. 7. Ga-In binary phase diagram……………………………………………………..13

Fig. 8. When the mole fraction of In less than the solubility limit……………………...14

Fig. 9. When the mole fraction of In greater than the solubility limit…………………..14

Fig. 10. Binary phase diagram for completely soluble system in both solid and liquid

State……………………………………………………………………………..16

Fig. 11. Binary phase diagram for system having limited solubility in solid state………16

Fig. 12. Cd-In binary phase diagram…………………………………………………….17

Fig. 13. The change of c/a ratio in In-Cd alloy with respect to composition at 25℃……18

Fig. 14. Spectra for 8N Ga w/ 111In at 290K……………………………………………..20

Fig. 15. The definition of B parameter…………………………………………………..21

Fig. 16. Scheme of run sequence on logarithm scale of Ga-In phase diagram………..…23

Fig. 17. Spectra for 8N Ga w/ 111In at 290K after one half-life………………………….24

Fig. 18. Spectra for 8N Ga w/ 111In at 290K after two half-lifes………………………...25

Fig. 19. Evolution of 푓푎푙푝ℎ푎;퐺푎 with background parameter…………………………..26

viii

Fig. 20. Spectra for Ga w/ 0.7 at.% natural In at 290K…………………………...27

Fig. 21. Change of the spectra of 111In crystal with temperature………………………29

Fig. 22. Temperature dependence of the percentage of the offset signal for 111In

Crystal………………………………………………………………………...29

Fig. 23. Lattice parameter and their ratio for indium microclusters as a function of average cluster diameter and number of atoms per cluster……………………30

Fig. 24. Comparison of Ga with only 111In and Ga with 0.7 at.% natural In…………...31

Fig. 25. Spectra of pure In metal at 288K………………………………………………32

Fig. 26. Spectra of In-Cd alloy with 3%Cd at 297K……………………………………33

Fig. 27. Average quadrupole interaction frequencies in an In alloy with 10 at.% Cd…..34

Fig. 28. Spectra of In-Cd alloy with 10%Cd at 300K, 273K and 100K………………...35

Fig. 29. Comparison of the mean quadrupole interaction frequencies in an In-Cd alloy (10%Cd) and in pure In metal………………………………………………….36

Fig. 30. Change of the frequency of In signal with time…………………………….…..37

Fig. 31. Spectra of Ga-Bi-111In ternary system at 200K…………………………………38

Fig. 32. Spectra of Ga-Cd-111In ternary system at 150K………………………………...38

Fig. 33. Spectra of Ga-Zn-111In ternary system at 150K…………………………………39

Fig. 34. Spectra of Ga-Sn-111In ternary system at 270K…………………………………39

Fig. 35. Fourier transformed spectra of Ga-Sn-In ternary system at 270K……………...40

Fig. 36. Reported Hg-rich region of Hg-In phase diagram………………………………41

Fig. 37. Fourier Spectra of Hg signal at 200K…………………………………………...42

Fig. 38. Spectra of Hg signal at 235K, 230K and 200K…………………………………42

Fig. 39. Evolution of Hg signal………………………………………………………….43

Fig. 40. Schematic Hg-In phase diagram at Hg-rich region consistent with

experiments…………………………………………………………………….43

Fig. 41. Temperature dependence of quadrupole interaction frequency of α-Ga……….48

Fig. 42. Temperature dependence of symmetry parameter of α-Ga…………………….49

Fig. 43. Quadrupole interaction frequency of α-Ga versus T3/2...... 50

Chapter 1: Introduction

Solubility of one metal in another can be extremely small and hard to measure. However, the solubility limit cannot be zero. [1] In order to measure this limit, very precise measurement need to be done. The method of perturbed angular correlation of gamma rays (PAC) has been used to determine site preferences, jump frequencies and much other information about solids. It has also been used to detect the solubility limit in solid. [2] Taking advantage of the 10-10 level of 111In radioisotope in the sample, it was possible to measure the extremely low solubility limit of indium in gallium.

Indium metal has the face-centered tetragonal crystal structure, but the unusual property that its crystal structure is face-centered cubic below the size of 2nm. The size distribution of indium cluster can be determined by this property. Cooling a binary alloy system below its eutectic temperature, the eutectic reaction occurs to transform the liquid phase into eutectic alloy. PAC is used to study the formation of eutectic alloy and how it coarsens over time. The growth of the size of indium cluster was observed by PAC.

Besides those two major subjects, other related interesting topics were also been studied in this work. Natural indium and other natural impurities were added to the system in order to see their effect on eutectic growth. In-Cd binary alloy at In-rich boundary was also studied. In-Hg binary system was measured as another example of studying solubility limit by PAC.

Chapter 2: Experimental Methods

2.1 PAC

2.1.1 Introduction to PAC Time differential perturbed γ-γ angular correlation spectroscopy is used to detect the location of indium probes in different phases and also the information of the structures of phases.

PAC probes usually have a relatively long-lived intermediate nuclear state within a γ-γ casade. The nucleus will have many precessions during this state due to the interaction with Electric Field Gradient (EFG) in the crystal. The start γ-rays and stop γ-rays are detected to measure the frequency of the precession of the nuclear spin during the intermediate state, and therefore determine the EFG at the location of the probe.

111In has a half-life of 2.81 days and decays to 111Cd by electron capture. Afterward, there is a long-lived intermediate state with spin I=5/2 and mean life time τ=120ns. This is the PAC level and it is sufficiently long for the PAC measurements.

Fig. 1. Decay of 111In to 111Cd

2.1.2 Instrumentation

Measurements were carried out using a fast-slow PAC spectrometer with four BaF4

2 scintillator detectors located at 90° surrounding the cold head of the close-cycle helium refrigerator. The heights of the detectors have been adjusted such that they are in the same plane of the sample.

Fast signals taken from the anodes of the photomultiplier tubes are used for timing. They are shaped with constant-fraction differential discriminators. Fast signals from detectors 1 and 2 start the time-to-amplitude converter (TAC). Fast signals from detectors 3 and 4, delayed by a digital delay generator (DDG), stop the TAC. Slow Signals taken from the dynodes are used to determine the energies of the γ-rays. They are amplified by AMP and discriminated by single-channel analyzers (SCA). Each pair of SCAs has two outputs leading to a logic unit. The output of the first SCA is true when the pulse height of input signal lies within the window of the start γ-ray. The output of the second SCA is true when the pulse height the input signal lies within the window of the stop γ-ray. The TAC is validated when one start and one stop γ-ray is detected. The routing signal tells analog to digital converter (ADC) in which memory unit to store the data. The memory units are connected to a PC from which the data can be analyzed.

Fig.2. PAC electronics schematic [3]

2.1.3 Data Analysis

The delayed coincidence spectra measured for a detector pair ij is

푡 퐶 (휃, 푡) = 푁 exp (− ) 푊(휃, 푡) + 퐵 (1) 푖푗 푖푗 휏 푖푗 in which τ is the mean life of the intermediate state, 푁푖푗 is the number of counts accumulated at time zero and 퐵푖푗 is the accidental background. 푊(휃, 푡) is the modulation of exponential decay from 111In to 111Cd.

The perturbation 퐺2(t) function can be obtained by [4]

2 √퐶13(휋,푡)퐶24(휋,푡);√퐶14(휋/2,푡)퐶23(휋/2,푡) 퐺2(푡) = ( ) (2) 퐴2훾푎 √퐶13(휋,푡)퐶24(휋,푡):√퐶14(휋/2,푡)퐶23(휋/2,푡)

The 퐺2(t) function is further fitted to

3 1 휔푛 푝 퐺2(푡) = 푠0 + ∑푛<1 푠푛 cos⁡(휔푛푡)exp⁡(− (휎 푡 )) (3) 2 휔1

For axial symmetric sample, the ratio of characteristic frequencies is

휔1: 휔2: 휔3 = 1: 2: 3 (4)

Also, 푠0 = 7/35,⁡푠1 = 13/35,⁡푠2 = 10/35 and ⁡푠3 = 5/35 are the amplitudes of the three harmonics when the sample is polycrystalline.

The hyperfine interaction parameter can therefore be obtained.

2.2 Closed-cycle Helium Refrigerator

2.2.1 Installation A CRYO-TORR® Pump and CRYODYNE® Refrigerator manufactured by CTI-CRYOGENICS were unused in our lab for about 15 years. In order to make low temperature measurements, the system was refurbished and connected in summer 2010. The system was composed by a Model 8300 compressor, a Model 8001 controller, a helium filtration cartridge, a cryopump, a roughing pump, a thermocouple gauge by Edwards, a T-2000 cryo controller by T.R.I. research, and accessories.

Fig. 3. The Configuration of Close Cycle Helium Refrigerator System

The system was connected as shown in Fig. 3. In order to make the old instrument work again, a lot of work was done. Rubber tubing worn out was replaced with new tygon tubing. This ensured a good vacuum seal especially between the roughing pump and cryopump. A new thermocouple gauge was installed to monitor the vacuum while running. Following the maintenance procedures, the helium filtration cartridge was replaced by a new one and the compressor was recharged with high purity helium gas. This should be done in the future when the helium pressure gauge reads at or below 245 psig.

2.2.2 Operation and Temperature Accuracy The sample was loaded on the stage of the cold head. To ensure good thermal contact, DOW CORNING® high vacuum grease was applied between the sample and the stage. The refrigerator together with the heater and sensors create a feedback system and therefore allow us to keep the sample at a certain temperature. After lots of running, we confirmed that the temperature stability is very good between 10K and 320K. Average fluctuation is about 0.1K.

The accuracy of the temperature was tested by the following measurement. For the sample of Ga with 0.7% of natural indium, the amount of natural indium is large so that we don’t need to worry about the form of small indium clusters. Therefore, the temperature we start to see indium signal is the eutectic temperature of Ga-In binary system. The

6 temperature we started to see In signal reads 289K. The temperature we see 100% indium signal reads 288K. Compared to the reported eutectic temperature of 288.5K, we are confirmed that the temperature accuracy is good. Also, we confirmed that the thermal gradient within the sample is less than 1K. Because most our measurements are in the range of 273K-320K, we decide that there is no need to do a temperature correction to the reading temperature.

2.3 Sample Preparation

2.3.1 Gallium with 111In Two types of Gallium metal was bought from manufactures. The 7N gallium (99.99999% Pure) is from Alfa Aesar and came in the form of 6mm diameter pellets. The 8N gallium (99.999999% Pure) is from Recapture Metals and came in a bottle. The 8N gallium has a certificate of analysis attached. According to the certificate, the amount of indium impurity is below 1 part-per-billion, which is under the detection limit. The 111In we 111 used is carrier free InCl3 solution purchased from Perkin-Elmer. 0.2mL HCL solution is 111 added to 2.0mci radioactivity in order to dilute the InCl3 solution.

7N Gallium was cut into small pieces with masses of about 100mg directly. 8N Gallium was first melted in a heated bath. A drop of gallium liquid was then removed from 111 the bottle and cooled to be crystallized. InCl3 solution was dropped directly on the surface of the gallium pieces and dried for about one hour. In order to diffuse 111In activity into gallium, samples were heated in a tube furnace. Samples were set in short quartz tubes to avoid contamination. The quartz tubes were set on alumina boats and then placed in the tube furnace. Hydrogen was flowed for five minutes before heating. Then the temperature was set to 250℃. The samples were heated at 250℃ for 1 hour with continuous hydrogen flow. After cooled to room temperature, samples were taken out of the furnace. For most of the cases, our gallium samples remained supercooled at room temperature for about 1 hour after being taken out of the furnace.

2.3.2 Gallium with 111In and ~1 at.% of other elements The sample preparation procedure is basically similar as mentioned in 1 except the following procedure.

After the gallium was cut and weighed, the weight of natural impurity was calculated. For In, Zn, Cd, Sn and Bi, a small piece was cut off from the metal foil and attached to the surface of Ga. For Hg, the volume was calculated and a microliter pipette was used to add a small drop of Hg to the surface of Ga. To melt the samples and diffuse 111In into the samples, different temperatures were set to according to the melting temperature of the natural impurities.

Natural Melting Diffusion Solute Temperature (℃) Temperature (℃) Hg -38.8 200 Bi 271.5 400 Zn 419.5 475 Cd 321.1 450 Sn 231.9 275 In 156.6 250 Table 1. Temperature to melt the samples

2.3.3 In-Cd Alloys The In-Cd alloys were prepared by arc melting. In order to get desired composition, In and Cd foil were cut and weighed carefully. 4 microliters of 111In solution was dropped on the surface of both of the metals and left to dry for about 1 hour. Cd was wrapped over by In to minimize potential evaporation of Cd. The package was set into the arc furnace. Arc melting was done with a direct current at 45A under the argon atmosphere. Sample formed into a sphere that was ready to measure.

Chapter 3: Theory

3.1 Crystal Structures of Ga, In and others

3.1.1 Gallium The pressure-temperature phase diagram shows that the stable phase for Ga at about 1atm and below 303K is α-Ga (See Fig.4, phase I). There are several metastable phases at below 255K. For example, β-Ga forms from supercooled liquid gallium below 255K. In our measurements, there was no evidence of any phase transitions from α-Ga to those metastable phases.

Fig. 4. Pressure-temperature phase diagram of Ga [5]

The crystal structure of α-Ga is complex compared to other metals. It is orthorhombic with 8 atoms in one unit cell (See Fig.5). The lattice parameters at 4.2K are

a=4.51Å b=4.49 Å c=9.65 Å

Each atom has one nearest neighbor at 2.44 Å.

Fig. 5. Crystal Structure of α-Ga [6]

When radioactive 111In atoms are in α-Ga phase, the PAC spectra exhibits a signature high frequency signal having a fundamental frequency at 139Mrad/s and η (the asymmetry parameter) of 0.2 due to the hyperfine interaction between the spin nuclei and the EFG inside the crystal. [7]

3.1.2 Indium

Under normal condition, indium has the face-centered tetragonal (fct) structure. It is a distortion of face-centered cubic (fcc) structure with a c/a ratio of about 1.07, slightly larger than the (fcc) structure ratio of 1.00.

Fig. 6. Crystal Structure of In [6]

The signature frequency for 111In being in indium fct crystal is about 17Mrad/s at room temperature with η=0. The change of the signature frequency of indium with respect to temperature is more significant than for most other metals.

3.1.3 Mercury, Tin and Cadmium Mercury has the lowest melting temperature among all metals. It crystallizes into a rhombohedral structure at 234.3K at 1 atm. Mercury has a signature frequency of 103Mrad/s with η=0 at 77K. [8]

Tin has two types of crystal structure at about 1 atm. At 13.2℃ or hotter, the stable phase is β-Sn, which appears to be silvery and metallic. Pure tin transformed slowly into α-Sn, a grey semiconductor phase below 13.2℃. However, the transition temperature is lower if there are impurities. β-Sn has a tetragonal structure with a signature frequency of about 35Mrad/s. α-Sn has a face-centered cubic structure. Therefore, a PAC spectra would show an offset signal if 111In gets into α-Sn phase due to the zero EFG.

Cadmium is a transition metal with a hexagonal close packed crystal structure. The signature frequency is 118Mrad/s at room temperature, with η=0.

To sum up, we are able to identify the PAC signals according to the table below. [9]

Metal Signature Frequency η

ω1(Mrad/s) (293K if not indicated) α-Gallium 136 0.2 Indium 17 0 Mercury 87 (225K) 0 β-Tin 35 0 Cadmium 118 0 Table 2. The identification of phases from PAC spectra

3.2 Binary phase diagram of Ga-In system and the calculation of the solubility

3.2.1 Binary phase diagram of Ga-In system The Ga-In binary phase diagram exhibits a eutectic with no intermetallic compounds. (See Fig.7) Above the liquidus curve, the system is in a uniform liquid phase of two mixture metals. Cooling below the liquidus curve, the system gets into A or B fields according to the composition. A is a mixture of liquid and solid gallium phase (Ga with very small amounts of In). B is a mixture of liquid phase and solid indium phase (In with a few percent of Ga solute). The eutectic temperature is at 288.5K. Cooling below the eutectic temperature, the system will become a eutectic alloy (or hypo-eutectic, hyper-eutectic alloy). I is the terminal solubility curve for Ga in In. From the phase diagram we can see that the solubility is at the level of a few percent. II is the solubility curve for In in Ga. In the phase diagram, it coincides with the axis, which means the solubility of In in solid α-Ga is not visible on this scale.

Fig. 7. Ga-In binary phase diagram [10]

In fact, the solubility of indium in alpha-gallium has been reported to be extremely small. According to the equilibrium phase diagram, there is no evidence of the formation of a Ga-rich solid solution. The reported solubility is less than an upper limit of 0.3% [10]. The 111In probe we used in PAC is less than at the part-per-billion level. Therefore, we are able to take advantage of this extremely low mole fraction to measure the solubility of In in solid α-Ga.

3.2.2 Method for determination of the terminal solubility Let us suppose that our sample is made to be Ga with only radioactive 111In added. The mole fraction of 111In is at less than the part-per-billion level and could be determined by analyzing the background signal. According to the Ga-In equilibrium phase diagram, the sample is in liquid state above the liquidus curve. Because the mole fraction of In is very low, the liquidus temperature should be very close to the melting temperature, which is 303K. Cooling the sample below the liquidus temperature, there are two possibilities.

A. If the mole fraction of In in α-Ga is less than the terminal solubility of In in α-Ga, all 111In will become incorporated in α-Ga, giving a 100% site fraction, as shown in Fig.8.

Fig. 8. When the mole fraction of In less than the solubility limit

B. If the mole fraction of In is greater than the terminal solubility but lower than the eutectic composition, the sample will be a mixture of solid α-Ga phase and liquid phase, as shown in Fig. 9. The volume fraction of the two phases can be determined by the level rule.

Fig. 9. When the mole fraction of In greater than the solubility limit

From the PAC measurements, in between the melting temperature of gallium and the eutectic temperature, one observed a combination of α-Ga signal and a constant anisotropy signal (offset signal) attributed to In probes being in the liquid phase. Therefore, we are in the case B. One can determine the solubility of In in α-Ga as follows.

Assume at some temperature T, the solubility of In in α-Ga is 푥푆. 푥푃 is the mole 111 fraction of In probes in the whole sample (solid plus liquid). 푥퐿 is the mole fraction of 111In in the liquid phase. According to the level rule, the mole fraction of the liquid phase is

푥푃;푥푆 푓푙푖푞 = (5) 푥퐿;푥푆

Let the total number of atoms in the sample be N. The number of 111In probes is just

N푥푃. The total number of atoms in liquid phase is N푓푙푖푞. The number of In atoms in liquid phase is N푓푙푖푞푥퐿. Therefore, the number of In atoms in solid phase is just N(푥푃 − 푓푙푖푞푥퐿). From the PAC measurements, we can get the fractions of indium in the solid and liquid phases. Denote the fraction of In in solid α-Ga phase as 푓훼.

N푥푃;N푓푙푖푞푥퐿 푥푃;푓푙푖푞푥퐿 푓훼 = = (6) N푥푃 푥푃

Because the solubility of indium in liquid gallium is much greater than in solid gallium, 푥퐿 ≫ 푥푆. Take this condition into account, we get, the approximation

푥푃;푥푆 푥푃;푥푆 푓푙푖푞 = = (7) 푥퐿;푥푆 푥퐿

Substituting (7) into (6), we get

푥푃;푓푙푖푞푥퐿 푥푆 푓훼 = = (8) 푥푃 푥푃

So that we found that 푓훼 is independent of 푥퐿.

One can measure 푓훼 directly in the experiments. We can also calculate 푥푃 from our background counting. Therefore, we are able to determine 푥푆, which is just the desired terminal solubility of indium in α-Ga.

3.3 Eutectic alloy and eutectic reaction The binary phase diagram of a system which is completely soluble in both liquid and solid phases looks like Fig. 10.

Fig. 10. Binary phase diagram for a completely soluble system in both solid and liquid states

However, mixing of A and B atoms in a solid solution is usually more difficult than in liquid. As a result of this difficulty, there is not only entropy of mixing but also enthalpy of mixing. The typical binary phase diagram in this case looks like Fig. 11.

Fig. 11. Binary phase diagram for system having limited solubilities in solid state

The eutectic temperature is the temperature below which the liquid phase disappears. If the composition of the system is just at the eutectic composition, cooling the system

16 below the eutectic temperature leads to the eutectic reaction

L → ⁡α + β (9)

The mixture of phase α + β is called the eutectic alloy.

If the composition of the system is below or above the eutectic composition, the reaction still takes place. The α or β phase will not be involved into the reaction. In other words, the reactant of the eutectic reaction is always the liquid phase. The alloy formed after the eutectic reaction is called hypo-eutectic or hyper-eutectic alloy if the composition before reaction is below or above the eutectic composition.

3.4 Crystal structures of indium alloyed with several percent of cadmium The binary phase diagram of In-Cd system is more complicated than a typical eutectic phase diagram. There are several intermediate compounds.

Fig. 12. Cd-In binary phase diagram [10]

In the In-rich region, if the mole fraction of Cd is less than about 5%, the stable

17 phase is the αT phase, with the same crystal structure as In metal, which has a face-centered tetragonal structure. Cd exists as defects in the In crystal. The c/a ratio is for pure In metal is 1.0762.

As the mole fraction of Cd increases beyond about 5 at.%, there exists a αK phase in a triangular field, which has a face-centered cubic structure. The c/a ratio is 1. The transformation between αT and αK phases is a so called martensitic transformation. The transformation from fct structure to fcc structure is simply a change of c/a ratio to minimize the crystal energy. Table 3 and Fig. 12 shows the change of c/a ratio with respect to composition at 25℃, made by X-ray analysis. [11] Phase Composition c/a at.% In

αK 89.8-93.8 1 95.6 1.0445 α (In) T 98.0 1.0641 100 1.0762

Table 3. The change of c/a ratio in In-Cd alloy with respect to composition at 25℃

Fig. 13. The change of c/a ratio in In-Cd alloy with respect to composition at 25℃ [11]

As one can see from the table, in αK phase, the c/a ratio stays constant. There is a

18 sudden jump of c/a ratio at the boundary of αK and αT phases. In αT phase, the c/a ratio decreases gradually with increasing Cd content. This table describes the phase transition across the composition boundary. Similarly, as we can see from the phase diagram, if we keep the composition (>6% Cd) as a constant but adjust the temperature, we will also see a phase transition between αK and αT phases.

Chapter 4: Experiments

4.1 Solubility of In in solid α-Ga

4.1.1 The measurement of solubility An alternative form of equation (8) from 3.2.2 is used to measure the terminal solubility.

푥푠 = 푓훼푥푃 (10)

To obtain 푥퐶 one needs to measure 푓훼 and 푥푃. The experiment is designed as following. A sample of 8N Gallium with only radioactive 111In added was made as described in 2.3.1. The sample was supercooled right after it was made. The mass was 102.43mg. The liquid sample was mounted on the stage of the Helium close-cycle refrigerator, with the temperature set to 290K. The sample was crystallized after about 30 minutes at 290K, after which PAC measurements were begun. During the measurement, temperature was maintained at 290K, which is between the eutectic temperature of Ga-In binary system and the melting temperature of Ga.

Fig.14 shows the measured spectra. The spectra was fitted to three components.

1.0

0.8

0.6

0.4

0.2

0.0 -300 -200 -100 0 100 200 300 t(ns)

Fig. 14. Specta for 8N Ga w/ 111In at 290K

The high frequency signal is for In probes that are dilute impurities in solid α-Ga phase. The offset signal is for In probes remaining in the liquid phase. The glitch signal in the center of the spectra is for left over In probes remaining on the surface of the stage from previous samples. The glitch signal did not change with time, therefore we fixed and subtracted this glitch signal as a background signal not relevant to the measurements. From the fitted spectra, we calculated that,

푓훼 = 0.133(8) (11) In order to calculate the amount of 111In probes in the sample, we saved a spectra after 5 hours to get the background parameter B. B is defined as the ratio of accidental counting to the true counting, which is shown in Fig. 15.

N True

N Accid t

Fig. 15. The definition of B parameter

111 Let Np be the number of In probes. The relation between B and Np is as following.

푁퐴푐푐푖푑 휏푁푢푐 B ≡ = 4푁푃 (12) 푁푇푟푢푒 휏푃푎푟푒푛푡

111 Where 휏푃푎푟푒푛푡 is the mean life time of the parent In radioisotope, [12]

2.8047 휏 = 푑푎푦푠 = 3.4960 × 105푠 (13) 푃푎푟푒푛푡 ln 2

휏푁푢푐 is the mean life of the PAC level, [12]

84.5 휏 = 푛푠 = 1.22 × 10;7푠 (14) 푁푢푐 ln 2

The factor of 4 is appropriate when double-sided spectra are collected.

Therefore,

퐵 휏푃푎푟푒푛푡 11 푁푃 = = 7.16 × 10 퐵 (15) 4 휏푁푢푐

From equation (13), B parameter is directly proportional to the amount of 111In probes in the sample.

Therefore,

푁푃 퐵 푥푃 = = 11 (16) 푁퐺푎 푛퐺푎×8.41×10

푛퐺푎 is the mole number of the Ga metal. For the first measurement, B=0.0810(3). ;3 The mass of Ga in the experiment is 102.43mg. So, 푛퐺푎 = 1.47 × 10 푚표푙푒푠 Hence,

;11 푥푃 = 6.55 × 10 (17) Therefore,

;12 푥푆 = 8.70 × 10 (18) To get this value, we have to assume that there is no natural indium in the sample. Therefore, this is a lower limit of the terminal solubility. We get to a conclusion that the solubility of indium in solid α-Ga is extremely small.

4.1.2 A test to determine the amount of natural indium Because the mole fraction of 111In probes added to the sample is only about 7 × 10;11, any natural indium as impurity in the 8N Ga will strongly affect the result. The MBE analysis provided by the manufacturer only ensures that the mole fraction of natural indium is less than 10-9 (the analytical detection limit). Therefore, it is necessary to find a

22 way to test the amount natural indium in our sample.

Our radioactive 111In probe has a half-life of about 2.8 days. So, after 2.8 days, the amount of 111In will decrease by half. Recall that

푥푆 푓α = (19) 푥푃

푥푆 is the terminal solubility of In in α-Ga, which is a constant. 푥푃 is the total amount 111 of In probes in the sample, which decreases with time. If 푥푃 decrease by half, 푓α will increase by a factor of two. However, once the α-Ga get crystallized, it is very difficult for indium diffuse back into the solid phase from the liquid. To observe the change of 푥푃, we re-melted the sample and recrystallized it at 290K.

After about one half-life, the temperature was raised to 325K to re-melt the sample. After 30 minutes, the temperature was set back to 290K. The sample remained supercooled at first and then crystallized to α-Ga after about 1 hour, as usual. PAC measurement was started after the sample crystallized. A Spectrum was saved after first five hours to get background parameter B.

The same procedure was repeated after another half-life. Therefore, three spectra were available for comparison.

Fig. 16. Scheme of run sequence on logarithm scale of Ga-In phase diagram

1.0

0.8

0.6

0.4

0.2

0.0 -300 -200 -100 0 100 200 300 t(ns)

Fig. 14. (copied) Spectra for 8N Ga w/ 111In at 290K

푓α = 0.133(8) B=0.0810(3)

1.0

0.8

0.6

0.4

0.2

0.0 -300 -200 -100 0 100 200 300 t(ns)

Fig. 17. Spectra for 8N Ga w/ 111In at 290K after one half-life

푓α = 0.293(7) B=0.0374(2)

1.0

0.8

0.6

0.4

0.2

0.0 -300 -200 -100 0 100 200 300 t(ns)

Fig. 18. Spectra for 8N Ga w/ 111In at 290K after two half-lifes

푓α = 0.376(17) B=0.0187(4) The glitch signal as background did not change during the experiment and was excluded from the analysis. In sequence of Fig. 14, 17, 18, we observed an increase of α-Ga signal and a decrease of the offset signal.

Assume the mole fraction of natural indium in the sample is 푥푁, which does not 111 change with time. The mole fraction of In probes in the sample is 푥푃, which decays with time as shown in equation (20).

푡 ; ⁄휏 푥푃 = 푥푃0푒 푃푎푟푒푛푡 (20)

As discussed in 4.1.1, 푥푃 can be obtained by the background parameter B.

퐵 ;10 푥푃 = 11 = 8.09 × 10 퐵 (21) 푛퐺푎×8.41×10

Considering this, equation (19) would be modified to

푥푠 푥푠 푓α = = −10 . (22) 푥푁:푥푃 푥푁:8.09×10 퐵

Results from fits of spectra in Fig. 14, 16, 17 can be fitted to (22) in order to get 푥푠

25 and 푥푁.

;12 푥푁 = 7.22 × 10 (23)

;12 푥푠 = 9.76 × 10 (24) Recall that 퐵 is a function of time.

푡 ; ⁄휏 퐵(푡) = 퐵0푒 푃푎푟푒푛푡 (25)

A plot of 푓α versus 퐵(푡) shows how 푓α evolves with time.

f 

0.4

0.3

 f

0.2

0.1 0.02 0.04 0.06 0.08 B(t)

Fig. 19. Evolution of 푓α with background parameter Since the radioactive 111In added into the sample at the beginning is

;11 푥푃0 = 6.55 × 10 (26) We confirmed that, natural In, if it existed, is about one tenth of the amount of 111In. The solubility of indium in solid α-Ga at 290K is on the order of 10-11. This confirms our assumption in 4.1.1 that the amount of natural In is negligible.

As shown in Fig.19., the fit was not very good. The difficulty of getting a good fit for

111 111 푥푠 and 푥푁 is mainly because of the short half-life of In probe. The half-life of In probe is only 2.8 days. It was almost impossible to get more data points after longer decay times as the sample became too weak to measure.

4.1.3 The effect by adding 0.7 at.% of natural In The terminal solubility of indium in solid α-Ga at 290K is a constant and close to 10-11. From (22) we know, if the total amount of In added to the sample is increased to -2 -9 10 level, 푓α measured from the experiment should be negligible (~10 ). A sample of Ga with 0.7% of natural In and also radioactive 111In added was made. From the measurement, no α-Ga signal was observed above the eutectic temperature. Only the offset signal due to the liquid gallium can be seen. This is consistent with our prediction.

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2 -500 -250 0 250 500 t(ns)

Fig. 20. Spectra for Ga w/ 0.7 at.% natural In at 290K

4.2 Coarsening of morphology of eutectic alloy

4.2.1 System having only 111In As discussed in 3.3, below the melting temperature of Ga and above the eutectic

27 temperature of Ga, the sample is a mixture of majority amount of α-Ga phase and extremely small pockets of liquid. At about 288K, the liquid is Ga with ~14 at.% 111In (see fig. 7.). The mole fraction of liquid pockets in the whole sample is only ~10-9. Cooling the sample below the eutectic temperature, the eutectic reaction occurs (see Fig. 11.),

L → ⁡α + β . (27)

The liquid phase in the sample, having the eutectic component, gradually turned into α-Ga phase and In metal phase. The eutectic temperature of Ga-In system is 288.5K and eutectic composition is 14.2 at.% In (see Fig. 7.). For the sample with only 10-10 level of 111In, a small portion of In signal starts to be observed at 285K. According to our measurements, In did not precipitate out at one temperature but in a range of 8K-10K. The percentage of In signal increases as temperature decreases while the percentage of offset decreases as temperature decreases. Below 275K, there was no offset signal left. In fig. 19., the α-Ga site fraction, about 10%, which was quenched in, has been subtracted off because it did not change with either temperature or time.

It is also interesting that the kinetics is not fully reversible. If the temperature is first set to 280K, when In has already formed into large enough crystal to see almost 100% indium metal signal, and then raised to 285K, the spectra did not change much from 280K. Only when it was heated to the eutectic temperature, we see 111In all being in liquid phase.

Ga 8N 1.0

0.5 285K

0.0 1.0

0.5 284K

0.0 1.0

0.5

282K

0.0 1.0

0.5 280K

0.0 1.0

0.5 275K

0.0

-500 -250 0 250 500 t(ns)

Fig. 21. Change of the spectra of 111In crystal with temperature

f Ga 8N Offset 1.2

1.0

0.8

0.6

Offset f 0.4

0.2

0.0 270 275 280 285 290 295 300 T (K)

Fig. 22. Temperature dependence of the percentage of the offset signal for 111In

crystal (Arrows show the consequence of measurements, first measurement was at 280K)

Below the eutectic temperature, there should be no liquid phase at all. The observed offset signal can only be due to the invisibility of small In cluster. Small In cluster whose size is below 5nm have fcc structure instead of fct structure.

Fig. 23. Lattice parameter and their ratio for indium microclusters as a function of average cluster diameter and number of atoms per cluster [13]

This will present an signal which is indistinguishable from 111In being in liquid. Therefore, the size distribution of indium cluster can be characterized qualitatively by 푓표푓푓푠푒푡. A smaller 푓표푓푓푠푒푡 means a size distribution having a larger mean size. The temperature difference between the measurement and eutectic temperatures is called the undercooling temperature. From Fig. 22., the size distribution is larger when the undercooling temperature is larger. In a binary eutectic alloy, both of the two component elements tend to grow larger to minimize the Gibbs free energy. The growth rate is proportional to the square of undercooling temperature. [14] Because of this kinetics, the trend shown in Fig. 22. is a function of both temperature and time.

Additional measurements have been done on determining the speed of forming larger crystals at a constant temperature. The kinetics of forming large crystals was observed to be very fast at 280K and below. It took less than a few hours to form crystals that were detectable by PAC. The kinetics at 286K, just below the eutectic temperature was observed to be very slow. The amplitude of In signal did not change after 3 days of measurement. However, the offset signal did decrease a little. A quantitative explanation of this complex behavior has not been found.

4.2.2 System having natural In By adding 0.7% of natural In, the liquid phase in the sample just above the eutectic temperature has a volume fraction of about 5%. This is macroscopic compared to the extremely small pools when there is only 111In (section 4.2.1). Therefore, it is much easier for In to grow into large crystals after the eutectic reaction. This is consistent with our measurements. This also proves that the temperature gradient is small in the sample so that the temperature difference within the sample is less than 1K.

Ga w/ 0.7% In Ga 1.2

1.0

0.8

0.6

Offset f 0.4

0.2

0.0

270 279 288 T (K)

Fig. 24. Comparison of Ga with only 111In and Ga with 0.7% natural In

4.3 EFG in In-Cd alloys The form of 111In crystal was observed in section 4.2.1. 111In has a half-life of 2.8 days and gradually decays into 111Cd. Hence, we would expect that after 2.8 days of measurement, half of the 111In atoms in the 111In crystal will become 111Cd atoms. To learn how Cd impurities affect the In signal, experiments were carried out to determine the crystal structures and quadrupole interactions of In-Cd Alloys with 0-10 at.% Cd. (see Fig. 12.)

Two samples of In-Cd alloys were made by the method described in 2.3.3. The nominal compositions of Cd were 3% and 10% respectively. Another pure In metal sample was made for comparison.

As expected, the pure In metal showed a well-defined quadrupole interaction signal at about 16.73(9)Mrad/s at 288K due to the EFG in the fct crystal structure as observed in previous measurements. [8]

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2 -500 -250 0 250 500 t(ns)

Fig. 25. Spectra of pure In metal at 288K

As temperature decreases, the frequency of the signal increases. In is one of the metals whose quadrupole interaction frequency is very sensitive to the temperature. In

32 has a Debye Temperature as low as 108K. Hence, the metal is soft so that its lattice parameter is very sensitive to temperature. Because EFG in the crystal is related to lattice parameter, the frequency of the signal of In is very sensitive to temperature.

In-Cd alloy with 3% Cd shows a signal very similar to pure In at room temperature, with the quadrupole interaction frequency at 16.26(8)Mrad/s.

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2 -500 -250 0 250 500 t(ns)

Fig. 26. Spectra of In-Cd alloy with 3%Cd at 297K

From the spectra we can see that 3% of Cd does not affect the In signal very much. However, this result is suspicious because Cd has a very low vapor pressure. Hence, it is likely that a lot of Cd has been lost during Arc melting.

To get a more convincing result, a sample with 10% Cd is made. In 3.4, we have shown that if the composition of Cd is from 6% to 20%, we would see a phase transition between αK (fcc) and αT (fct) phases by adjusting temperature. Above the transition temperature, the alloy is in pure αK phase. Below the transition temperature, the alloy is a mixture of Cd-rich phase and In-rich phase, which is similar to the eutectic alloy.

At 300K, an extremely low frequency signal at 8.35(11)Mrad/s is observed with η 111 fixed to 0.6. This is attributed to In being in αK phase. The EFG is produced by the distribution of Cd impurities in the cubic structure.

Cooling to 273K, a signal at 13.21(10)Mrad/s is observed instead of the previous 111 low frequency signal. This is attributed to In being in αT phase. The sudden jump of the frequency shows the phase transition occurring between 273K and 300K. The phase transition is observed to be very fast at 273K. This is because in Martensitic transformation, the only change is the c/a ratio. The reversibility is also confirmed in our experiments.

12 fct

(Mrad/s) 

 8 fcc

0 100 200 300 T (K)

Fig. 27. Average quadrupole interaction frequencies in an In alloy with 10 at.% Cd

The data shows the phase transition from αT (fct) to αK (fcc) at ~20℃(see Fig.12).

1.0

0.5 300K

0.0

1.0

0.5 273K

0.0

1.0

0.5 100K

0.0

-500 -250 0 250 500 t(ns)

Fig. 28. Spectra of an In-Cd alloy with 10%Cd at 300K, 273K and 100K

The frequency of the signal in the alloy is about 19% lower than in In metal. There are two possible reasons. One is the c/a ratio decreases as the mole fraction of Cd increases. This will lead to a smaller frequency. Another reason is the EFG in the crystal was changed by replacing In atoms into Cd atoms. The direction of this effect needs further calculation.

As temperature decreases, the frequency of this signal increases as in pure In. The comparison of the quadrupole interaction frequency in In-Cd alloy (10%Cd) and pure In metal is shown in Fig. 28..

In-Cd Alloy 10% Cd 25 Pure In (Christiansen [15]) Pure In (This work)

(Mrad/s)

1 

100 200 300 T (K)

Fig. 29. Comparison of the mean quadrupole interaction frequencies in an In-Cd alloy (10%Cd) and in pure In metal

We got to a conclusion that the effect that Cd impurities have on In signal is to decrease the frequency of In signal. Once a sample of Ga with 111In is freshly made and cooled below the eutectic temperature, the mole fraction of Cd in In metal phase is approximately zero. As 111In decays into 111Cd, the frequency of In signal was observed to decrease with time. The set of measurement shown in Fig. 29. was made on a new sample at 286K other than the one discussed in 4.2.1. The background parameter was used to characterize the ratio of In that had decayed into Cd. After the mole fraction of Cd exceeds the solubility limit of Cd in In, the change of frequency is still continuous. One possible reason is that the αT phase becomes metastable after exceeding the limit. However, the Cd atom remains in the position of 111In atom before decaying. Therefore the continuous change is attributed to the change of c/a ratio and/or the EFG disturbances produced by Cd impurities. Another possible reason is that Cd was excluded from the αT phase, leading to a smaller size distribution of αT crystals. This may also lead to an increasing of frequency.

(Mrad/s)

1  15

14 1.0 0.8 0.6 0.4 Percentage of decay

Fig. 30. Change of the frequency of In signal with time

4.4 The effect on forming eutectic alloy by adding other natural impurities A Ga-111In binary system was studied in which the mole fraction of In is extremely low. A eutectic alloy forms below the eutectic temperature, with In precipitating out, forming small crystals. Cooling further, the small crystals gradually grew to large crystals to show In metal signal.

If about 1% of another composition X is added to the system, a ternary system will be formed. Similar to In, the third metal X will precipitate out in crystals below the eutectic temperature of X-Ga. Because the composition of 111In is extremely small, it is unlikely that it will affect the eutectic temperature of X-Ga.

Experiments were carried out in which about 1% of Bi, Cd, Zn, Sn and Hg were added to the system respectively. Different behaviors were observed.

For Bi, Zn and Cd, a damped In signal was observed. In this case, the precipitation of In was not strongly affected by the third composition X. The damping of the In signal is due to junk introduced by the third compositions since the purity of those metals is not as high as 8N Ga. Especially in the samples with Zn or Bi added, no α-Ga signal was

37 observed at all. This is because the mole fraction of In impurity from Zn metal is high enough to depress the α-Ga signal as discussed in equation (22).

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2 -500 -250 0 250 500 t(ns)

Fig. 31. Spectra of Ga-Bi-111In ternary system at 200K

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2 -500 -250 0 250 500 t(ns)

Fig. 32. Spectra of Ga-Cd-111In ternary system at 150K

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2 -500 -250 0 250 500 t(ns)

Fig. 33. Spectra of Ga-Zn-111In ternary system at 150K

For Sn, damped Sn signal was observed. This shows that 111In has incorporated into Sn crystals.

1.2

1.0

0.8

0.6

0.4

0.2

0.0

-0.2 -500 -250 0 250 500 t(ns)

Fig. 34. Spectra of Ga-Sn-111In ternary system at 270K

It is clearer to distinguish this damped Sn signal from In signal by Fourier transformed spectra. The fitted frequency is 41.73(63)Mrad/s compared to the In signal having about 17Mrad/s at this temperature.

1.0

0.8

0.6

0.4

0.2

0.0 0 50 100 150 200 250 300 350 400 450 500 Mrad/s

Fig. 35. Fourier transformed spectra of Ga-Sn-In ternary system at 270K

For Hg, above the melting temperature of Hg, only offset signal was observed. Below the melting temperature, well defined Hg signal gradually appears. This behavior will be discussed in the next section.

Different behaviors are summed up in the table below.

Metal X Eutectic temperature of Signal Observed below eutectic X-Ga (℃) temperature Bi 29.48 Damped Indium Signal Cd 29.38 Damped Indium Signal Zn 24.67 Damped Indium Signal Sn 20.5 Damped Tin Signal In 15.3 Undamped Indium Signal Hg <-73 Undamped Mercury Signal Table 4. Signal observed in Ga-X-In ternary system

A tentative explanation is given as following. For Bi, Cd and Zn, the eutectic temperature of X-Ga is 10-15℃ above In-Ga. Therefore, cooling the sample down to the

40 eutectic temperature of X-Ga, X will first precipitates out while In still remains in the liquid phase. Cooling to 15.3℃, In will precipitate out independently because X has already grown into large crystals. For Sn, the eutectic temperature of Sn-Ga is only 5℃ above In-Ga. At 15.3℃, Sn crystals may have not been well grown. Therefore, below 15.3℃, In atoms will have chance to incorporate into the Sn crystal and show a damped Sn signal.

4.5 Hg-rich region of the Hg-In binary system The solid solubility of In in Hg has been reported to be very small. [10] On the Hg-rich region of existed phase diagram, the liquidus line on the Hg side was terminated as following. No eutectic behavior was observed on the Hg-rich boundary. However, this is not agreed with our experiment.

Fig. 36. Reported Hg-rich region of Hg-In phase diagram

A sample with about 100mg Ga, 0.4μL Hg and 111In probe was made. Gallium was believed to be crystallized into α-Ga and exclude almost all In probes into liquid phase below 280K. Therefore, we have almost an In-Hg binary system. The mole fraction of In in this system is calculated to be 1.13x10-8. Cooling below the liquidus curve, according to the phase diagram above, we should see 100% mercury signal immediately. However, we see the Hg signal with quadrupole interaction frequency at about 75Mrad/s grows gradually through a range of temperature from 230K to 200K. At 200K and below, we see 100% Hg signal with no offset component.

0 0 50 100 150 200 250 300 350 400 450 500 Mrad/s

Fig. 37. Fourier Spectra of Hg signal at 200K

1.2

0.8 235K

0.4

0.0 1.2

0.8 230K 0.4

0.0 1.2

0.8

200K 0.4

0.0

-500 -250 0 250 500 t(ns)

Fig. 38. Spectra of Hg signal at 235K, 230K and 200K

f LIQ 1.2

1.0

0.8

0.6

0.4

0.2

0.0

140 160 180 200 220 240 T (K)

Fig. 39. Evolution of Hg signal

Therefore, we think the there is a eutectic point very close to solid Hg phase. There is also a eutectic temperature below the melting temperature of Hg. The phase diagram should look like following,

Fig. 40. Schematic Hg-In phase diagram at Hg-rich region consistent with experiments

According to Fig. 40., cooling below the liquidus curve, Hg-In binary system reaches a mixture phase of liquid and Hg-rich solid. Therefore, a mixture of Hg signal and offset signal is expected. As temperature decreases, Hg signal increases according to the level rule. In Ga-In system, α-Ga signal never increases to 100% because the mole fraction of In is larger than the solubility limit. In that case, the measurements show a mixture of α-Ga phase and In-rich phase. However, in Hg-In system, we observed that the Hg signal reaches 100% at 200K. This indicates that the mole fraction of In, which is ~1.1x10-8, is below the solubility limit. From this fact, we conclude that the solubility of In in Hg between 150K and 235K is larger than 1.1x10-8. We also know that the eutectic temperature of Hg-In system is below 200K.

Chapter 5: Summary

The method of perturbed angular correlation of gamma rays (PAC) was used for the first time to determine the solubility of one metal in another. The measured solubility of indium in solid gallium phase at 290K is about 10-11. The solubility of indium in solid mercury phase is larger than 10-8.

The forming of eutectic alloy from the liquid phase is also studied. 111In radioactive crystal is observed from the spectra. Temperature dependence of the size distribution of 111In crystal is observed. The kinetics of forming larger crystals is also studied tentatively. The effect on forming eutectic alloy by adding other natural impurities was observed in the experiments. Co-precipitation occurs when the eutectic temperature of the two systems is closed.

In-Cd alloy at In-rich boundary was studied. Phase transition between αT and αK 111 phases are observed. In being in αK phase express a low frequency signal at about 111 8Mrad/s. In being in αT phase express a signal similar to indium metal signal with a frequency 20% lower than in bulk indium metal.

APPENDICES

A. Two mysteries in the literature solved [16] 1. Mysterious 22.4Mrad/s signal reported for 111Cd in α-Ga at 77K

A comprehensive study was carried out by H. Haas and D. A. Shirley [8] on determination of quadrupole interactions in metals by PAC. Quadrupole interaction frequencies of 14 types of radioisotopes including 111Cd (decays from 111In) in several host metals were measured. Most of the data in this paper was repeated by many other experiments and proved to be very accurate. [9] The only data strongly inconsistent with other experiments is for 111Cd in α-Ga at 77K. The reported quadrupole interaction frequency is 22.4Mrad/s. Another data for 111Cd in α-Ga at 293K is 142Mrad/s [9]. Although the temperatures of the two measurements are different, the temperature dependence of quadrupole frequency has never been observed to be so huge. Moreover, the 22.4Mrad/s frequency is very close to the frequency for 111Cd in In metal at 77K, which is 23.0Mrad/s reported in the same paper. As discussed in section 4.2.1, below eutectic temperature, 111In probes precipitate out from tiny liquid pools and form 111In crystals, exhibiting In metal signal. Therefore, we concluded that the 22.4Mrad/s signal observed by H. Haas et al. was not for 111Cd in α-Ga, but for 111Cd in radioactive 111In crystals.

2. Mysterious “missing anisotropy” in experiments on α-Ga at 293K

In a study of EFG for 111Cd in α-Ga at 293K [7], the amplitude of α-Ga signal

(132Mrad/s) was about 25% if assuming γa to be a typical value of 0.7. Unlike the

G2(t) function we used, method used to extract R(t) ratio function is insensitive to unperturbed anisotropy (as seen in liquids). So, the unexpected small amplitude of α-Ga signal indicates a missing of anisotropy signal. As discussed in section 4.1.1, above eutectic temperature, the sample is a mixture of solid α-Ga phase and liquid phase (see Fig.9). The “missing anisotropy” was just for 111Cd in liquid phase. In our measurements, α-Ga signal was about 13% above eutectic temperature. Since the

46 sample made in ref [7] had a mass of 180mg, about twice as much as our samples. We would have expected the amplitude of the signal in ref [7] to be 26%. So, the measurements are quite consistent.

B. Temperature dependence of quadrupole interaction frequency of α-Ga Temperature dependence of the electric field gradients in Cd, In and Sn was studied in ref [15]. We made measurements on α-Ga phase at different temperatures. Temperature dependence of quadrupole interaction frequency and symmetric parameter of α-Ga are presented here.

Temperature(K) ω1 (Mrad/s) η 20 145.96(95) 0.205(5) 77 144.77(52) 0.205(5) 150 142.40(43) 0.190(5) 200 140.54(36) 0.210(5) 260 137.94(42) 0.205(5) 275 137.17(76) 0.235(10) 285 136.34(69) 0.220(10) Table 5. Temperature dependence of quadrupole interaction frequency and symmetric parameter of α-Ga

 (Mrad/s)  148

144

(Mrad/s) 140





136

0 100 200 300 T(K)

Fig. 41. Temperature dependence of quadrupole interaction frequency of α-Ga

 0.5

0.4

0.3

 0.2

0.1

0.0 0 100 200 300 T(K)

Fig. 42. Temperature dependence of symmetry parameter of α-Ga

In ref [9], the quadrupole interaction frequencies were plotted versus T3/2 to get a 3/2 linear relation. In the case of α-Ga, a plot of ω1 versus T also leads to a good linear behavior. The data was also fitted to

푝 휔1 = 휔10 − 퐵푇 . (28) The fitted power,

p = 1.50(8) (29)

is very close to 3/2.

 MRad/s) 

144

140

(Mrad/s)

 

136

0 2000 4000 6000 3/2 T Fig. 43. Quadrupole interaction frequency of α-Ga versus T3/2

BIBLIOGRAPHY

1. Alloy Phase Equilibria, A. Prince, Elsevier Publishing Company, 1966, p.74

2. G. J. Kemerink, F. Pleiter and G. H. Kruithof, Hyperfine Interactions 35, 619-622, 1987

3. John Bevington, Lattice locations and diffusion in intermetallic compounds explored through PAC measurements and DFT calculations, PhD Dissertation, Washington State University, May 2011 (unpublished)

4. A.R. Arends et al., Hyperfine Interaction 8191, 1980

5. Lucia Comez and Andrea Di Cicco, Phys. Rev. B 65, 014114, 2001

6. http://cst-www.nrl.navy.mil/lattice/ Naval Research Laboratory

7. M. Menningen, H. Haas and H. Rinneberg, Phys. Rev. B 35, 8378, 1987

8. H. Haas and D. A. Shirley, J. Chem. Phys. 58, 3339, 1973

9. R. Vianden, Hyperfine Interactions IV, 956-976, 1978 10. Binary Alloys Phase diagrams, Thaddeus B. Massalski, 2nd ed., ASM, Materials Park, Ohio (1990).

11. A Handbook of Lattice Spacings and Structures of Metals and Alloys, W. B. Pearson, Pergamon Press, 483

12. http://www.nndc.bnl.gov/ National Nuclear Data Center

13. A. Yokozeki and G. B. Stein, J. Appl. Phys. 49(4), 1978

14. H. L. Lukas, E. T. Henig and B. Zimmerman, Calphad 1 (3), 225-236, 1977

15. J. Christiansen, P. Heubes, R. Keitel, W. Klinger, W. Loeffler, W. Sandner and W. Witthuhn, Z Physik B 24, 177-187, 1976

16. Heinz Haas, private communication, 2011