A Thesis Presented To The Faculty of Alfred University
X-RAY DETECTION THRESHOLD OF CRYSTALLINE PARTICLES IN AMORPHOUS SOLIDS
By
Shannon R. Rogers
In partial fulfillment of the requirements for
the Alfred University Honors Program December 7, 2019
Under the Supervision of:
Chair:
_____________________________________________________________
William M Carty Ph.D.
Committee Members:
___________________________________________________________
__
Hyojin Lee
___________________________________________________________
__
Mackenzie Stevens
ii
Acknowledgements
Special thanks to everyone I learned from throughout this project. Thank you to Dr. Carty for the thesis idea and guidance and pushing me to present at my first conference. Thank you to Mackenzie Rigatoni for her help with sample prep, glass pouring for opacity testing, and emotional support. Thank you to Hyojin Lee for help with XRD analysis. Thank you to Swavek Zdzieszynski for help when the D2 Phaser malfunctioned. Thank you to Dr. Sundarum for
accepting my abstract to present my data at MS&T 2019 for the first time in the Glass and Optical Materials Symposium. Thank you to Dan Delia for Microsoft Word Formatting tips and tricks. Special thanks to Krishna Amin for everything else!
iii
Table of Contents
Acknowledgements ...ii
List of Figures ...iv
List of Tables ... v
Abstract ...vi
Introduction ... 1
Background ... 2
Result & Discussion ... 9
Summary and Conclusions ... 19
References ... 20
iv
List of Figures
Figure 1. X-ray diffractometer schematic.3 ... 3
Figure 2. Messier and Deguire, 1984: Glasses containing (a) 6.3 at. % N and (b,b') 13.3 at. % N. All specimens approximately 2mm thick. The glass in (b') was formulated with AlN rather than Si3N4. [1] ... 5
Figure 3. Density relationship to detection threshold. ... 11
Figure 4. Particle size relationship to detection threshold. ... 12
Figure 5. Comparison of diffraction peak characteristics for CeO2. ... 13
Figure 6. Detection ability as a function of diffraction intensity. ... 14
Figure 7. Transmissivity and detection threshold of Si3N4 in barium frit and container glass. ... 15
Figure 8. Si3N4 in container glass detection limit determined by the 100% peak denoted with a circle at 35.3̊ 2θ of (A) 0.3v/o pre-melt (B) >3.0v/o post- melt ... 16
Figure 9. Si3N4 in barium frit detection limit determined by the 100% peak denoted with a circle at 35.3̊ 2θ of (A) 3.0v/o pre-melt (B) >3.0v/o post- melt ... 18
v
List of Tables
Table I. Material Properties of Crystalline Particles ... 9 Table II. Detection threshold relationship with crystal to glass density ratio ... 10 Table III. PDF Card and Miller indices [hkl] of crystalline particles at the 100%
peak. ... 10
vi Abstract
It is relatively common to refer to glass samples as “completely
amorphous” when the correct term should be “X-ray amorphous” meaning that crystalline particles are not detectable by X-ray diffraction. The threshold
detection limit of crystalline material in a glass is dependent on several variables including the particle size, molecular weight of the glass, and the diffraction efficiency of the crystalline particle. Several powders, including Al2O3, ZrO2, ZrSiO4, quartz (SiO2), SiC, CeO2 and Si3N4, were mixed (via milling) with commercial glass frits ranging from 0.1 to 3.0 volume percent (v/o) and then measured with powder X-ray diffraction. The particle size and density of the crystalline powders was varied while keeping the volume fraction similar. The results show that the average atomic number of the glass frit contributes to X-ray scattering significantly increasing the detection threshold for crystalline particles.
Introduction
The technique of X-ray diffraction of crystalline particles has evolved over the years. Messier and Deguire (1984) published about “glass” that had low transmissivity and was translucent to opaque.1 Their definition of glass was not well defined, and it is unclear if their glasses were in fact X-ray amorphous.
Today X-ray diffraction can detect crystalline particles at lower concentration than was possible in 1984. There are a few properties that effect this detection
threshold. It is hypothesized that detection threshold of crystalline particles in glass is a function of glass density with a direct relationship. As the density of the glass frit increases, the detection threshold for crystalline particles in glass frit increases. X-rays can be absorbed into the amorphous background of glasses at a high density more easily than lower density frits, masking the detection of crystalline particles in the glass frit compact at low concentrations. The size of crystalline particle plays a small factor in detection threshold if the particles are small enough to exhibit x-ray peak broadening. The density of the crystalline particle plays a role in detection limit, as the molecular weight of the crystal increases the detection limit decreases. Some crystals however, such as quartz have a high diffraction efficiency. The 100% peak in x-ray diffraction spectra has high count and diffracts easily. This plays a factor in crystalline detection ability at low concentrations in glass frits. The factors of glass frit density, crystalline
particle density, crystalline particle size, crystal diffraction efficiency all play a role in the detection ability of crystalline particles in amorphous solids.
2
Background
X-Ray diffraction is a useful tool to a wide range of scientists including metallurgists, chemists, ceramists, physicists and more. The discovery that X- rays could be used to analyze the structure of crystals was first discovered made by Laue in 1912 and was a breakthrough in materials research.2 Today X-rays are used for more characterization than just crystal structure including chemical analysis, stress measurements, the study of phase equilibria, particle size, and crystallographic orientation. X-ray diffractometers have been used to solve complex problems and has made major advances for the field of material science, but diffraction did not used to be as easy as it is today. X-ray characterization has a seen a stark evolution of diffraction techniques.
Modern X-ray diffraction is rather simple to use, operate, and analyze data. First use of the technique resulted in hours and hours of developing films and comparing it to literature to analyze results. Use of X-ray diffraction today, seen in equipment such as Bruker’s D2 Phaser or Siemens D500 in Alfred University labs, the operation is rather simple. Students and faculty pack their sample specimen into a disk on top of a flat surface, and the sample compact is analyzed on the flat surface. The sample being analyzed must be as flat as possible to ensure there is no experimental shift during diffraction. The sample is placed on the diffractometer stage, which is a device for rotating the crystalline sample and the detector so the diffraction pattern can be documented by the control of a computer.
3
In simple terms, X-ray characterization can occur either by EDS (electron dispersive spectroscopy) or XRD (X-ray diffraction). In EDS, X-rays are beamed at the crystalline sample, electrons in the sample are expelled by the X-rays.
Each sample will give off a characteristic energy as the electrons are expelled which is indicative of the material chemistry. This characteristic energy and intensity are picked up by the detector. In XRD a primary X-ray is diffracted off a crystalline surface and a diffracted/secondary X-ray beam is picked up by a detection source (Figure 1). The operator sets the angle 2θ range they want the sample rotated to and the step size and count time. This means that the sample surface is measured at an angle to the X-ray and detection source, the angle where the measurement is changed at a certain increment set and held for a set amount of time. These parameters must be kept the same between samples that are being compared.
Figure 1. X-ray diffractometer schematic.3
For crystalline diffraction, not only is an X-ray production source
necessary, which is Cu Kα or Mo Kα in modern diffractometers, but the detection of X-rays is just as necessary. B.D. Cullity describes the fluorescent screens, and
4
photographic films that have been used to detect X-rays in the past, and counters that are used today.2 Fluorescent screens are composed of a thin layer of zinc sulfide, with trace amounts of nickel, tacked to cardboard. The material
fluoresces under the action of X-rays hitting it producing light in the visible region, specifically yellow to locate the position of the beam. Photographic films develop in a similar way to how light changes film in film camera. The amount of
blackening caused by x-ray light is dependent on intensity which depend on wavelength. This is characteristic of the material being diffracted by the x-ray source. Today x-ray diffractometers use counters which convert x-rays into a pulsating electric current. The number of pulses recorded is indicative of the diffracted beam intensity. The pulsating current can be analyzed by a computer.
Counter types include proportional, scintillation and semiconductor, which can be used for quantitative work, rather than photographic film which just delivers results of relative intensity.
The topic of detection threshold of crystalline particles in amorphous solids was sparked from an article by Messier and Deguire published in 1984.1 The high transparency of high nitrogen (13.3%) glasses was found to reduced by the presence of silicon precipitates resulting from thermal decomposition during melting in their study. Figure 1 shows Messier and Deguire’s reported glass sample for qualitative transparency. The dark grey color of glass (b) is said to be due to metallic particles from Si3N4 which does not come from the AlN doped glass which is more transmissive (b’). In glass (b) a strength limiting defect in a bend specimen was identified as Si, causing the darker color. The concentration
5
of these particles is unknown. The Si particles were attempted to be eliminated by changing processing conditions.
Figure 2. Messier and Deguire, 1984: Glasses containing (a) 6.3 at. % N and (b & b') 13.3 at. % N. All specimens approximately 2mm thick. The glass in (b') was formulated with AlN rather than Si3N4.1
Since 1984, x-ray diffraction techniques have improved to detect
crystalline particles at lower concentrations. There are a few causes for opacity or reduced transmission in glasses including light scattering of particles,
scattering from pores or bubbles, phase separation, band gap energy,
absorption-wavelength etc.4 Glass frits with known concentrations of crystalline particles were melted and tested for optical transmissivity. The compositions of glass frits and low crystalline particle concentrations were diffracted for crystalline peak detection threshold before and after melting.
Crystalline particles to be detectable at 3% concentration to determine structural information at a depth of 10 microns in a two-phase sample.5 X-ray diffraction is non-destructive, and can provide information on phase and defects,
6
as well as strain, crystal orientation and size. Materials of any element can be studied using x-ray diffraction but, but it is most sensitive to elements with a high- Z number (high molecular weight) since the diffraction intensity is much larger than low-Z elements.
X-ray diffraction occurs when the source is scattered by long range order in crystalline materials. Glasses however are defined as have no long-range order, and do not produce high intensity peak diffraction patterns. Instead, glasses are detected as broad peaks or “amorphous humps” in x-ray spectra.
Crystalline peaks of particles added in low concentrations to glass can be absorbed by the glass background 6. Diffraction peaks are correlated to the crystallographic orientation or Miller indices denoted as [hkl]. Each peak in an X- ray spectrum is a different orientation for that crystalline plane.
Braggs Law (Equation 1) is the basis for X-ray diffraction instruments used today, which was developed after Bragg used diffraction to determine rock salt structure.7 It is the order of reflection time the wavelength of x-rays equal to two times the identity period of the set of reflecting net planes of atoms and the sinusoidal relationship to the angle of glancing. Terms of Bragg’s law are defined as: n=order (integer “1,2,3…”), λ=wavelength, d=spacing between layers of atoms, θ=angle of diffraction.
nλ=2dsinθ (1)
7
Experimental Procedure
Sample Prep
Commercially available barium and bismuth frits were obtained, as well as soda lime silicate (container glass) frit by crushing Ball canning jars. The density of each of the three glass frits was measured using a pycnometer method
(AccuPyc II, Micrometrics, Norcross, GA, USA) He Pycnometer. Several crystalline powders, including Al2O3 (3 different commercially available particle sizes), (pseudo-boehmite derived) Al2O3, ZrO2, ZrSiO4, Si3N4, CeO2 (2 different particle sizes), SiC, and SiO2 (quartz), were added to each of the glass frits. The crystalline particles were measured for density in the He Pycnometer and
measured for specific surface area (SSA) (Gemini VII, Micrometrics, Norcross, GA, USA) BET. The density and SSA of each crystalline particle powder was used to calculate the average D50 diameter for particle size. Each crystalline particle was batched with container glass in 0.1, 0.3, 1.0 and 3.0 volume percent (v/o) concentrations batches. ZrSiO4, Al2O3, and Si3N4 were batched with barium frit in 0.1, 0.3, 1.0 and 3.0 volume percent (v/o) concentrations batches. CeO2, Al2O3 (pseudo-boehmite derived), and Al2O3 (A16) were batched with bismuth frit in 0.1, 0.3, 1.0 and 3.0 volume percent (v/o) concentrations batches. All batches of crystalline particle and glass frit samples were mixed using an automatic mortar and pestle to ensure homogeneity of the mixture.
8 Peak Detection
Each sample was diffracted using an x-ray diffractometer (D2 Phaser, Bruker, Karlsruhe, Germany 2010) with a Cu Kα X-ray source, in a 1” diameter ring and clip sample holder with a 2 second count time, 0.04 step size over a 60 degrees 2θ range. The 100% crystalline powder samples were also measured.
The 100% peak for each sample was identified by the PDF database and used the main peak for identifying the detection threshold. Each diffraction pattern was loaded into JADE (Material Data, 2013), and the area under the 100% peak for each crystal type was attempted to be identified. If the area was able to be measured, the lowest concentration at which crystalline peaks could be detected was determined to be the “detection threshold”. The diffraction pattern for each level of particle concentration in a series was plotted in stacked peaks. The detection threshold of each crystalline particle and glass frit combination was documented and plotted against the calculated D50 (Equation 2) values of
crystalline particles, the diffraction efficiency of each crystalline particles, and the crystal to glass density ratio.
𝐷 =
6𝑆𝑆𝐴 ∙𝜌 (2)
9
Result & Discussion Material Characterization
Each crystalline powder and glass frit used were characterized. Table I displays laboratory measured values for specific surface area and density were determined and used to calculate the average diameter for particle size. The peak intensity of each crystalline particle is representative of crystalline diffraction efficiency, with quartz (SiO2) having the highest intensity peak.
Table I. Material Properties of Crystalline Particles Material Properties
Crystal
SSA (m2/g)
Density (g/cm3)
D50 (μm)
I/Io of 100% Peak (intensity counts x103)
[hkl]
Al2O3 21.3 4.00 1.13 30.6 [113]
CeO2 30.0 7.24 1.45 20.9 [111]
CeO2 2.60 7.24 16.9 84.8 [111]
ZrO2 6.70 5.90 5.32 24.9 [111]
ZrSiO4 1.50 4.70 19.2 151 [200]
Al2O3 8.50 3.95 2.79 30.6 [113]
Al2O3 4.90 3.95 4.84 30.6 [113]
Al2O3 1.00 3.95 24.9 30.6 [113]
Si3N4 10.4 3.30 1.90 14.4 [210]
SiC 0.40 3.20 52.6 65.2 [102]
SiO2 1.50 2.70 11.1 295 [101]
The density of container glass, barium frit, and bismuth frit is 2.5g/cm3, 3.3 g/cm3, and 4.4 g/cm3 respectively. The detection threshold is observed to
correlate crystalline particle to glass density ratio. Density ratios are presented in Table II.
10
Table II. Detection threshold relationship with crystal to glass density ratio Detection Threshold (vol %) Crystal/Glass Density Ratio Crystal D50
(μm)
Container Glass
Barium Frit
Bismuth Frit
Container Glass
Barium Frit
Bismuth Frit
Al2O3 1.13 0.3 0.3 3.0 2.90 2.19 1.65
CeO2 1.45 0.1 0.3 2.90 2.19 1.65
CeO2 16.93 0.1 2.36 1.79 1.34
ZrO2 5.32 0.1 1.08 0.82 0.61
ZrSiO4 19.26 0.1 0.1 1.58 1.20 0.90
Al2O3 2.79 0.3 1.0 1.58 1.20 0.90
Al2O3 4.84 0.3 1.60 1.21 0.91
Al2O3 24.95 0.3 1.58 1.20 0.90
Si3N4 1.9 0.3 3.0 1.28 0.97 0.73
SiC 52.6 0.3 1.88 1.42 1.07
SiO2 11.08 0.1 1.32 1.00 0.75
The powder diffraction file (PDF) card was pulled for each crystalline powder from the ICDD (International Centre for Diffraction Data) database (Table III).
Table III. PDF Card and Miller indices [hkl] of crystalline particles at the 100%
peak.
Crystal PDF Card 100% Peak 2θ [hkl]
Si3N4 00-009-0250 35.2 [210]
Al2O3 00-010-0173 43.4 [113]
ZrSiO2 00-006-0266 26.98 [200]
ZrO2 00-007-0343 28.21 [111]
SiO2 00-012-0708 26.3 [101]
SiC 00-022-1273 35.7 [102]
CeO2 00-004-0593 28.5 [111]
11 Density Relationship to Detection Threshold
The density of the crystalline particle was compared to the density of glass as a ratio. As the density of crystalline particle to glass ratio increases, the
detection threshold decreases (Figure 3). The detection threshold of Al2O3, CeO2
and Si3N4 particles increases as the density of the glass increases.
Figure 3. Density relationship to detection threshold.
Particle Size Relationship to Detection Threshold
The particle size of the crystalline solids is a factor in X-ray detection in glass frits because small particles can experience peak broadening in x-ray diffraction spectra. There is a weak relationship observed between particle size and detection limit. The detection limit is observed to increase as the calculated D50 decreases presented in Figure 4.
0.1 1 10
0.5 1 1.5 2 2.5 3
Detection Threshold (Vol %)
Density of Crystal to Density of Glass Ratio Container Glass
Barium Frit Bismuth Frit
12
Figure 4. Particle size relationship to detection threshold.
The CeO2 powders used had significantly different measured specific surface areas of 30.0m2/g and 2.6 m2/g, with a calculated D50 of 1.45μm and 16.9μm respectively. The 16.9μm powder exhibited peak broadening as
illustrated in Figure 5. With peak broadening more drastic in small particle sizes, the detection threshold for that crystalline particle increases as the peak is absorbed or masked by the amorphous hump from the glass in the background at low concentrations.
0.1 1 10
1.0 10.0 100.0
Detection Threshold (Vol %)
Average Calculated D50 (microns)
Container Glass Barium Frit Bismuth Frit
13
Figure 5. Comparison of diffraction peak characteristics for CeO2.
Diffraction Effectiveness Relationship to Detection Threshold
Crystalline materials like SiO2 (quartz) have a higher diffraction efficiency which increases the detection ability due to a high intensity 100% peak.
Crystalline particles with a higher diffraction efficiency can be detected at lower concentrations as shown in Figure 6. It is observed that diffraction efficiency has a stronger relationship with detection threshold than particle density, because quartz was easily detected at the lowest concentration of 0.1v/o due to have the highest diffraction efficiency.
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Figure 6. Detection ability as a function of diffraction intensity.
Melted Glasses for Optical Transmissivity Testing
The pre-melted samples proved to be detected at particle concentration thresholds of 0.1 to 3.0 volume present based on a variety of factors. The samples that were diffracted post-melting however could not be detected for crystalline peaks at these low concentrations, even above 10 volume percent. It is hypothesized that the low transmissivity observed in these glass samples is not due to particle concentrations, but some factor that effects opacity.
The experimental matrix for glass melts was limited, but Si3N4 was measured and melted in container glass and barium frit (Figure 7). The coloring varied between glass type at the same concentration, and bubbles were visible in the container glass samples.
0.1 1 10
10 100 1000
Detection Threshold (vol%)
Intensity of 100% Peak (Counts, peak intensity)
Container Glass Barium Frit Bismuth Frit
15
Figure 7. Transmissivity and detection threshold of Si3N4 in barium frit and container glass.
The detection threshold observed in Figure 8 was determined by the homogenized glass frit and crystalline material before melting, since it was known exactly what the concentration of crystalline particles was. In these glass samples, the 100% peak for Si3N4 at 35.3̊ 2θ was detected at 0.3v/o is indicated by the line with a circular tip, in container glass seen in Figure 8A. Once the glass was melted however, the Si3N4 particles dissolved into the glass structure and were not detectable up to 3.0 v/o and predictably higher (Figure 8B).
16 A
B
Figure 8. Si3N4 in container glass detection limit determined by the 100% peak denoted with a circle at 35.3̊ 2θ of (A) 0.3v/o pre-melt (B) >3.0v/o post-melt.
17
Figures 10 and 11 show the X-ray diffraction spectra for Si3N4 in barium frit pre-melt and post melt respectively. The barium frit was found to have undissolved quartz crystals which were absent in the post melt spectra, yet the detection threshold of Si3N4 increased to 3.0v/o due to the increased density of the barium frit compared to container glass, along with optical transmissivity.
18 A
B
Figure 9. Si3N4 in barium frit detection limit determined by the 100% peak denoted with a circle at 35.3̊ 2θ of (A) 3.0v/o pre-melt (B) >3.0v/o post-melt.
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Summary and Conclusions
The x-ray detection threshold for crystalline particles in glass frits observed to have a direct relationship with glass density, and an indirect
relationship with particle size, crystalline diffraction efficiency, and crystal to glass density ratio. While X-ray Peak broadening is present with small particle sizes but does not appear to influence detection threshold. The peak intensity of the 100%
peak of each crystal plays a critical role in detection ability. Quartz had the highest diffraction efficiency and was able to be detected at the lowest concentration of 1.0v/o. Crystalline particle inclusions alter the transmissivity below the detection threshold.
20 References
1. D. Messier and E. Deguire, Thermal Decomposition in the System Si-Y- Al-O-N, Watertown, Massachusets: Army Materials and Mechanics Research Center, 1984.
2. Cullity, Elements of X-Ray Diffraction, Reading, Massachusetts: Addision- Wesley Publishing Company, Inc , 1978.
3. T. Kukuchi, "Single Crystal Orientation Measurement by X-Ray Methods,"
Rigaku Corporation, Tokyo, Japan, 1990.
4. C. R. Brundle, C. Evans and S. Wilson, Encylcopedia of Materials Characterization: Surfaces, Interfaces, Thin Films, Boston: Butterworth- Heinemann, 1992.
5. H. M. N.S. Murthy, General procedure for evaluating amorphous
scattering and crystallinity from X-ray diffraction scans of semicrystalline polymers, Morristown, NJ: Corporate Technology, Allied-Signal Inc., 1989.
6. S. Borisov and N. Podberezskaya, "X-ray diffraction analysis: A brief history and achievements of the first century," Journal of Structural Chemistry, vol. 53, no. 1573-8779, pp. 1-3, 01 Dec 2012.
7. S. L. Bragg, The Development of X-Ray Analysis, New York: Dover Publication, Inc., 1975.
