Influences of composition, melt viscosity and crystallization on the color strength and stability of multi-oxide glass f...


Material Information

Influences of composition, melt viscosity and crystallization on the color strength and stability of multi-oxide glass frit/zircon-vanadium pigment systems for ceramic whitewares coatings applications
Physical Description:
xxi, 367 leaves : ill. ; 29 cm.
Earl, David A., 1961-
Publication Date:


Subjects / Keywords:
Materials Science and Engineering thesis, Ph.D   ( lcsh )
Dissertations, Academic -- Materials Science and Engineering -- UF   ( lcsh )
bibliography   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph.D.)--University of Florida, 1998.
Includes bibliographical references (leaves 359-366).
General Note:
General Note:
Statement of Responsibility:
by David A. Earl.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 030019851
oclc - 40878780
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Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
    Table of Contents
        Page iv
        Page v
        Page vi
        Page vii
    List of Tables
        Page viii
        Page ix
    List of Figures
        Page x
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    Chapter 1. Introduction
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    Chapter 2. Background
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    Chapter 3. Experimental procedures
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    Chapter 4. Results
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    Chapter 5. Discussion
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    Chapter 6. Summary and conclusions
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    Chapter 7. Future work
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    Appendix A. Units for describing light and color
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    Appendix B. The 15 causes of color
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    Appendix C. Density, particle size and application weight data
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    Appendix D. Data from coatings batched with frit, 2.5% bentonite and Zr-V pigment, and fired using a 45-minute ceramic tile cycle
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    Appendix E. Frit spectral reflectance data and curves at each temperature and pigment loading
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    Biographical sketch
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Full Text








I am grateful for the guidance and inspiration provided

by Dr. David E. Clark, chairman of my supervisory committee.

My association with Dr. Clark has greatly enhanced my

academic, professional and personal growth over the past five


I would like to thank Dr. Joseph Simmons, Dr. E. Dow

Whitney, Dr. Jack Mecholsky and Dr. Dinesh Shah for

participating on my supervisory committee. Thanks also go to

Kristie Leiser, Mark Moore, Robert DiFiori, Diane Folz and

Rebecca Schulz of Dr. Clark's research group for their


In addition I would like to acknowledge the industrial

support of this research. I would like to thank Florida Tile

Industries; Bob Blonski, Klaus Meinssen, Bruno Burzacchini

and Marzia Barrattini of Ferro Corporation; and Dan Swiler,

Hong Chen and Pam Lucas of Ceredec Corporation.

Finally, and most importantly, I am grateful for the

patience and encouragement of my wife, Jacquie. This

research effort would not have been possible without her





ACKNOWLEDGMENTS ........................................... ii

LIST OF TABLES ........................................... viii

LIST OF FIGURES............................................. x

ABSTRACT..................................................... xix


1. INTRODUCTION ........................................ 1

1.1 Color in the Ceramics Industry .................... 1
1.2 Glaze Colorants ................................ 5
1.3 Potential Influence of Frit ......................... 7
1.4 Overview of Dissertation Goals .................... 12
1.5 Guide for Using This Dissertation ................. 16

2. BACKGROUND .......................................... 21

2.1 Color Theory ........................................ 21
2.1.1 Light and the Visible Spectrum ......... 22
2.1.2 Materials Interactions with Light ...... 29
2.1.2a Refraction ........................... 30
2.1.2b Surface Reflection and Gloss ...... 36
2.1.2c Opacity and Translucency ............ 42
2.1.2d Absorption, Transmission and
Color ................................... 51
2.1.3 Color Perception by the Human Eye ...... 60
2.1.4 Color Measurement ......................... 65
2.1.4a Spectrophotometry .................... 65
2.1.4b Basis for Color Quantification .... 72
2.1.4c CIE L*a*b* Measurement Scale ...... 78

2.2 Color in Ceramic Glazes ........................... 86
2.2.1 Silicate Glass Structures and
Properties .................................. 87
2.2.2 Glaze Base Materials and Formulas ...... 99
2.2.3 Fast-Fire Whiteware Glazes and Frits... 105
2.2.4 Ceramic Colorants ......................... 113
2.2.4a Zircon Triaxial Pigments ............ 115
2.2.4b Kubelka-Munk Analysis of
Colorant Layers ............................. 127
2.2.5 Frit Influence on Color Development .... 132
2.2.5a Crystallization Mechanisms ........ 132
2.2.5b Zircon Crystallization and
Dissolution ............................. 145
2.2.5c Liquid-Liquid Phase Separation .... 152
2.2.5d Viscosity Relationships ............. 155

3. EXPERIMENTAL PROCEDURES ............................ 161

3.1 Materials and Methods ............................. 161
3.1.1 Glass Frits and Zr-V Pigment ............. 161
3.1.2 Coatings Preparation and Application... 165
3.1.3 Firing Curves .......................... 167
3.2 Materials Characterization and Analytical
Techniques .................................. 169
3.2.1 AAS and XRF ............................ 169
3.2.2 Frit Density Determination ............... 169
3.2.3 Laser Diffraction Particle Size
Analysis .................................... 170
3.2.4 Spectrophotometry and Color
Calculations ................................ 170
3.2.5 Gloss Measurements ........................ 172
3.2.6 Heating Microscopy ........................ 173
3.2.7 Dilatometry ............................ 174
3.2.8 X-Ray Diffraction (XRD) ................... 174
3.2.9 Scanning Electron Microscopy (SEM) and
Energy Dispersive X-Ray Spectroscopy (EDS).. 176
3.3 Statistical Methods for Deriving Equations .... 177

4. RESULTS ............................................ 180

4.1 Frit and Pigment Properties ...................... 180
4.2 Color of Fired Coatings ........................... 181
4.2.1 Spectral Reflectance Curves .............. 182
4.2.2 Pigment Absorption Factors (K/S) ......... 188

4.2.3 Color in L*, a* and b* Values ............ 193
4.2.4 Color Stability ........................... 206
4.2.5 Specular Gloss ............................. 208
4.3 Viscosity of Coatings During Heating ............ 210
4.3.1 Heating Microscope Images ................ 210
4.3.2 Dilatometric Tg and T2 ................... 213
4.3.3 Viscosity vs. Temperature ................ 216
4.4 Derived Statistical Models ....................... 219
4.4.1 K/S vs. Coating Composition and
Temperature ................................. 220
4.4.2 AE* vs. Coating Composition .............. 235
4.4.3 Log Viscosity vs. Coating Composition
and Temperature ............................. 244
4.5 Evolved Crystalline Species ...................... 246
4.5.1 XRD, SEM and EDS Evaluations ............. 246
4.5.1a Frits with ZrO2 ...................... 246
4.5.1b Frits without ZrO2 ................... 260
4.5.2 Zircon Quantitative Analysis ............. 277
4.5.2a Frits with ZrO2 and ZnO ............. 280
4.5.2b Frits with ZrO2 and SrO ............. 280
4.5.2c Frits without ZrO2 ................... 281

5. DISCUSSION ......................................... 282

5.1 Color Strength and Stability Dependency ....... 282
5.1.1 Coating Composition ....................... 284
5.1.1a Zr-V Loading ......................... 284
5.1.1b ZrO2 .............................. 286
5.1.1c SrO vs. ZnO .......................... 290
5.1.!d A1203/Alkalis ....................... 293
5.1.2 Crystalline Species ....................... 296
5.1.2a Zircon ............................ 296
5.1.2b Diopside ............................. 305
5.1.2c Hardystonite ......................... 307
5.1.2d Strontium Calcium Silicate ........ 308
5.2 Melt Viscosity ................................ 312
5.2.1 Influence on Crystallization and
Zr-V Dissolution ........................ 312
5.2.2 Value as a Predictor of K/S and E* .... 315

6. SUMMARY AND CONCLUSIONS ............................

6.1 Zr-V Pigment and Color Values .................
6.2 Frit Oxide Composition ........................
6.3 Viscosity, Crystallization and Zr-V
Dissolution ......................................

7. FUTURE WORK ........................................



B THE 15 CAUSES OF COLOR .............................


45-MINUTE CERAMIC TILE CYCLE .....................


REFERENCES ..............................................

BIOGRAPHICAL SKETCH .....................................














Table Pace

1.1 Example of Ceramic Coatings Applications on a
Decorated Floor Tile ........................... 8

1.2 Variables That Influence Ceramic Glaze Color ...... 9

2.1 Index of Refraction of Selected Materials at
589 nm Wavelength in Air ....................... 32

2.2 Properties of Materials Used for Opacifying
Ceramic Glazes ................................. 45

2.3 Transition Elements and Their Properties .......... 58

2.4 Factors for Uniform Color Scales for Normalizing
to a Standard Reference White .................. 81

2.5 Glass Formers, Intermediates and Modifiers
Materials Commonly Employed in Whiteware
Glazes .......................................... 92

2.6 Properties Associated with the Presence of
Various Oxides in Glass ........................ 98

2.7 Common Ceramic Tile Glaze Base Materials .......... 100

2.8 Examples of Compositions (Weight %) of Commercial
Glazes ......................................... 1 01

2.9 Summary of Important Glaze Properties and
Characteristics ................................ 102

2.10 Seger's Formula for Classifying Glazes ............ 103

2.11 Typical Empirical Formulas, in Molar Equivalents,
for Fast-Fire Gloss and Matte Glazes ............ ill


2.12 Glaze Pigments and Their Requirements ............. 117

3.1 Frits Investigated ................................ 162

E.1 Engobe and Frits A and B Reflectance Data ......... 347

E.2 Frits C and D Reflectance Data .................... 348

E.3 Frits E and F Reflectance Data .................... 349

E.4 Frits G and H Reflectance Data .................... 350


Figure Pace

1.1 Flow chart summary of main research variables ..... 17

2.1 Electromagnetic spectrum .......................... 25

2.2 Wavelength vs. energy distribution of daylight .... 26

2.3 Refractive index vs. wavelength of incident
light for three glasses ......................... 34

2.4 Reflection and transmission of light by a glassy
material containing suspended particles ......... 37

2.5 Fresnel reflection for a) an air/glass boundary
and b) total reflectivity for different index
of refraction ................................... 40

2.6 Reflectance vs. wavelength of light for a TiO2
opacified white glaze fired to 10000C, at
various glaze application weights in g/ft2 ...... 50

2.7 The 5 d orbitals .................................. 57

2.8 Human optical system .............................. 61

2.9 Luminosity functions of the rods (nighttime
scotopic vision) and cones (daytime photopic
vision) of the human eye ........................ 63

2.10 Reflectance versus wavelength for opaque coatings
colored with pigments that absorb a portion of
incident light .................................. 67

2.11 Basic components of spectrophotometers ............ 69

2.12 Schematic of the Hardy spectrophotometer .......... 70

2.13 Weighting functions used for the standard
observer at a 20 field of view .................. 74

2.14 Luminosity or lightness (Y) and chromaticity
(x, y) MacAdam limits for colors viewed in
daylight ........................................ 79

2.15 Schematic of L*a*b* color space ................... 83

2.16 Comparison of structures and XRD patterns of
crystalline and vitreous silica ................. 90

2.17 Two-dimensional representation of modifiers
(a) Na 1 and (b) Ca+2 in the silicate glass
structure ....................................... 95

2.18 Inorganic pigment family .......................... 114

2.19 CIE a* and b* chroma of ceramic pigments .......... 116

2.20 Typical forms of zircon crystals. (a-c): a{ 1001
m{110}, p I01}, x{211} ; and zircon lattice
structure (d,e) ................................. 120

2.21 Splitting of the d orbital in V+4 by tetrahedral
(Td) and tetragonal (D2d) crystal fields ......... 124

2.22 Schematic of basis for Kubelka-Munk analysis of
colorant layers ................................. 128

2.23 Relationship between viscosity and temperature
favoring nucleation and growth in glazes ........ 137

2.24 Crystal growth rate as a function of temperature
in Na20-CaO-Al20l-SiO2 glass ..................... 144

2.25 Binary phase diagram of ZrO2 and Si02 system ...... 149

2.26 Viscosities of some commercial silicate glasses... 157

3.1 Time-temperature profiles used to fire the tiles.. 168

4.1 Spectral reflectance of unfired raw materials and
the engobe substrate backing .................... 183

4.2 Spectral reflectance of coatings batched with
frit C, fired to 1000'C ......................... 186

4.3 Spectral reflectance of coatings batched with
frit H, fired to 1100C ......................... 187

4.4 Spectral reflectance of coatings batched with
2.0% Zr-V, fired to 1000*C ...................... 189

4.5 Spectral reflectance of coatings batched with
2.0% Zr-V, fired to 1050'C ...................... 190

4.6 Spectral reflectance of coatings batched with
2.0% Zr-V, fired to 1100'C ...................... 191

4.7 Pigment absorption factors versus weight percent
Zr-V batched in coatings fired to 1000C, 1050C
and 1100*C peak temperature ..................... 192

4.8 Color values of coatings batched with frits
(A-H) and Zr-V pigment, and fired to 1050C ..... 194

4.9 Color values of coatings batched with frits
(A-H) and Zr-V pigment, and fired to I100C ..... 195

4.10 Color values of coatings batched with frits
!A-H) and no Zr-V, and fired to 1000'C, 1050C
or 1100'C ....................................... 198

4.11 Color values of coatings batched with frits
(A-H) and 0.5% Zr-V, and fired to 1000'C, 1050'C
or 1100C ....................................... 199

4.12 Color values of coatings batched with frits
(A-H) and 2.0% Zr-V and fired to 1000'C, 1050C
or 1100C ....................................... 200


4.13 Color values of coatings batched with frits
(A-H) and 5.0% Zr-V, and fired to 1000'C, 1050'C
or 1100 C ....................................... 201

4.14 Relationship between lightness (L*) and blueness
(-b*) of coatings batched with Zr-V pigment and
fired to 10000C, 10500C and 1100'C peak
temperature ..................................... 203

4.15 Zr-V pigment absorption factor relationships
with L*, a* and b* color values of fired
coatings ........................................ 205

4.16 Color changes (AE*) due to a variation in peak
firing temperature from 10500C to 11000C for
coatings batched with frits (A-H) and Zr-V
pigment ......................................... 207

4.17 Specular gloss of fired coatings at a 60' angle
of incidence .................................... 209

4.18 Heating microscope images of coatings batched
with frits (A-H) and 2.0% Zr-V, at 900'C, 1000'C
and 11000C ...................................... 211

4.19 Heating microscope images of characteristic
stages of flow of coatings batched with frits
(A-H) and 2.0% Zr-V ............................. 212

4.20 Thermal dilatometric analyses of coatings A-D
batched with 2.0% Zr-V .......................... 214

4.21 Thermal dilatometric analyses of coatings E-H
batched with 2.0% Zr-V .......................... 215

4.22 Log il versus temperature of coatings batched with
2.0% Zr-V. Frits A-D incorporate 8% ZrO2 ....... 217

4.23 Log 'q versus temperature of coatings batched with
2.0% Zr-V. Frits E-H contain no ZrO2 ........... 218


4.24 Pigment absorption factor actual and equation
(4.2) predicted results for fired coatings
batched with 2.0% Zr-V ............................. 224

4.25 Individual effects of frit oxides on K/S based on
statistical model (4.2) for 2.0% Zr-V and a
peak firing temperature of 10500C................. 225

4.26 Variables weight of influence on K/S, based on
statistical models 4.1 (0.5% Zr-V), 4.2
(2% Zr-V) and 4.3 (5% Zr-V) ........................ 228

4.27 Pigment absorption factor trends with frit
A1203:alkalis ratio of coatings batched with
2.0% Zr-V and fired to 10000C, 1050'C or I100'C. 229

4.28 Pigment absorption factor versus frit ZnO and
SrO molar equivalents of fired coatings batched
with 2.0% Zr-V and fired to 10000C, 1050'C or
1100C peak temperature ............................ 230

4.29 influence of frit ZrO2, in the presence of SrO or
ZnO, on K/S of fired coatings batched with 2.0%
Zr-V and fired to 10000C, 10500C or 11000C ...... 231

4.30 Variations in pigment absorption factor (K/S) due
to changes in peak firing temperature, for
coatings watched with 2.0% Zr-V and frits
containing 8% ZrO2 versus 0% ZrO2 .................. 232

4.31 Delta E* actual and equation (4.7) predicted
results for fired coatings batched with 2.0%
Zr-V ............................................ 239

4.32 Individual effects of frit oxides on Delta E*,
based on statistical model 4.7 for 2.0% Zr-V .... 240

4.33 Variables weight of influence on Delta E*, based
on statistical models 4.6 (0.5% Zr-V), 4.7
(2.0% Zr-V) and 4.8 (5.0% Zr-V) .................... 242


4.34 Color changes due to variations in peak firing
temperature and frit A1203:alkali ratio of
coatings batched with 2.0% Zr-V ................... 243

4.35 XRD patterns from coatings batched with frit A
and 2.0% Zr-V, and fired to 1000'C, 1050'C and
11000C. Frit A includes 8% ZrO2, 12% ZnO,
0% SrO, 5% alkalis .............................. 247

4.36 SEM micrographs of a coating batched with frit A
and 2.0% Zr-V, and fired to 11000C.
Magnification is (a) X 1,000 and (b) X 6,000.
Shown are large Zr-V particles surrounded by
fine zircon precipitates ........................... 248

4.37 XRD patterns from coatings batched with frit B
and 2.0% Zr-V, and fired to 10000C, 1050'C and
11000C. Frit B includes 8% ZrO2, 12% ZnO,
0% SrO, 10% alkalis ............................. 249

4.38 SEM micrographs of a coating batched with frit B
and 2.0% Zr-V, and fired to 11000C.
Magnification is (a) X 1,000 and (b) X 6,000.
Shown are large Zr-V particles, fine zircon
precipitates and large zircon fibers .............. 250

4.39 XRD patterns from coatings batched with frit C
and 2.0% Zr-V, and fired to 10000C, 10500C and
I100'C. Frit C includes 8% ZrO2, 0% ZnO,
12% SrO, 5% alkalis ............................. 251

4.40 XRD patterns from coatings batched with frit D
and 2.0% Zr-V, and fired to 10000C, 10500C and
11000C. Frit D includes 8% ZrO2, 0% ZnO,
12% SrO, 10% alkalis ............................ 252

4.41 SEM micrographs of coatings batched with 2.0%
Zr-V, (a) frit C and (b) frit D, and fired to
11000C. (magnification X 1,000). Particles
shown are Zr-V pigment .............................. 253

4.42 X-ray diffraction profile for zircon, ZrSiO4 ...... 255


4.43 SEM micrograph of zircon-vanadium (Zr-V) pigment,
Ceredec 41715A, X 1,000 magnification ............. 256

4.44 XRD patterns from coatings batched with frit E
and 2.0% Zr-V, and fired to 1000'C, 10500C and
1100'C. Frit E includes 0% ZrO2, 12% ZnO,
0% SrO and 5% alkalis ........................... 261

4.45 SEM micrograph of a coating batched with frit
E and 2.0% Zr-V, and fired to 1050'C.
Magnification is X 1,000. Shown are large
Zr-V particles surrounded by dispersed diopside. 262

4.46 XRD patterns from coatings batched with frit
F and 2.0% Zr-V, and fired to 10000C, 10500C
and 11000C. Frit F includes 0% ZrO2, 12% ZnO,
0% SrO and 10% alkalis .......................... 263

4.47 SEM micrographs of a coating batched with frit
F and 2.0% Zr-V, and fired to 11000C.
Magnification is (a) X 1,000 and (b) 6,000.
All particles shown are hardystonite .............. 264

4.48 XRD patterns from coatings batched with frit G
and 2.0% Zr-V, and fired to 10000C, 10500C and
11000C. Frit G includes 0% ZrO2, 0% ZnO, 12%
SrO and 5% alkalis .............................. 265

4.49 SEM micrograph of a coating batched with frit
G and 2.0% Zr-V, fired to 11000C (magnification
X 1,000). Shown is crystallized SrCa2Si3O9 ...... 266

4.50 XRD patterns from coatings batched with frit
H and 2.0% Zr-V, and fired to 10000C, 10500C
and 11000C. Frit H includes 0% ZrO2, 0% ZnO,
12% SrO and 10% alkalis ............................ 267

4.51 SEM micrographs of a coating batched with frit
H and 2.0% Zr-V, and fired to 11000C.
Magnification is (a) X 1,000 and (b) X 6,000.
Shown is crystallized SrCa2Si3O9 ................. .. 268


4.52 Relationship between XRD [312] integrated
intensity and weight percent zircon in unfired
coatings ........................................ 278

4.53 Weight percent zircon in fired coatings batched
with 2.0% Zr-V .................................. 279

5.1 Changes in reflectance distributions at 400 nm
and 640 nm wavelengths due to increases in peak
firing temperature for coatings batched with
0.5%, 2.0% and 5.0% Zr-V ....................... 285

5.2 Influence of frit density on the color stability
of coatings batched with 2.0% Zr-V pigment ...... 289

5.3 Pigment absorption factors (K/S) for coatings
batched with Zr-V pigment and frits containing
8% ZrO2, and fired to 10000C, 10500C or 11000C
peak temperature ................................ 291

5.4 Visual lightness (L*), greenness (-a*) and
blueness (-b*) as a function of weight percent
zircon in the fired coatings batched with 2.0%
Zr-V ............................................ 299

5.5 Pigment absorption factor (K/S) as a function of
Zr-V pigment and zircon contents in coatings
batched with 2.0% Zr-V .......................... 302

5.6 Changes in color stability denoted by K/S and
Delta E*, as a function of weight percent
zircon in coatings batched with 2.0% Zr-V ....... 304

5.7 Colcr lightness (L*) and blueness (-b*)
progression with diopside crystallization
and pigment dissolution in coatings batched
with frit E and 2.0% Zr-V ....................... 306

5.8 Color lightness (L*) and blueness (-b*)
progression with hardystonite crystallization
and pigment dissolution in coatings batched
with frit F and 2.0% Zr-V ....................... 309


5.9 Color lightness (L*) and blueness (-b*)
progression with SrCa2Si3O9 crystallization
and pigment dissolution in coatings batched
with 2.0% Zr-V .................................. 311

5.10 Integrated log viscosity from 700'C to 11000C
versus fired color strength (K/S) and stability
(Delta E*) in coatings batched with 2.0% Zr-V... 316

5.11 Slope in the log viscosity versus temperature
near the softening point versus fired color
strength (K/S) and stability (Delta E*) in
coatings batched with 2.0% Zr-V ................. 318

E.1 Frit A spectral reflectance curves ................ 351

E.2 Frit B spectral reflectance curves ................ 352

E.3 Frit C spectral reflectance curves ................ 353

E.4 Frit D spectral reflectance curves ................ 354

E.5 Frit E spectral reflectance curves ................ 355

E.6 Frit F spectral reflectance curves ................ 356

E.7 Frit G spectral reflectance curves ................ 357

E.8 Frit H spectral reflectance curves ................ 358


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy



David A. Earl

December 1998

Chairman: David E. Clark
Major Department: Materials Science and Engineering

Color control is becoming increasingly important in the

industrial processing of ceramics coatings. Multi-oxide

glass frits are the predominant materials in ceramic

whitewares coatings, and zircon doped pigments are the most

commonly used colorants.

The primary objective of this research was to determine

if glass frits could be formulated to improve the fired color

strength and high-temperature stability of ceramic coatings

colored with zircon-vanadium (Zr-V) blue pigments. The

results would also be applicable to other ceramic pigments

that utilize the same zircon structure to incorporate


colorant metal ions. A secondary goal was to relate the frit

oxide composition, pigment content, firing temperature, melt

viscosity and microstructural development to the fired color.

A ceramic tile process was applied to fabricate sample

coatings for the study. A coating's color was quantified and

related to human perception with CIE L*, a* and b* values and

pigment absorption factors (K/S), calculated based on

spectral reflectance data.

The research was successful in quantifying the influence

of individual glass frit oxides on the fired color strength

and high-temperature stability of the coatings. Opaque and

transparent glossy frit compositions which yield excellent

color strength and stability were formulated. Mathematical

models for predicting a coating's color strength and

stability given the frit oxide composition, Zr-V pigment

loading and peak firing temperature were derived. Frit

oxides of ZrO2, SrO, ZnO, A1203, Na20 and K20 were found to

have a significant influence on crystallization, pigment

dissolution and color development. The properties, sizes,

morphologies and quantities of crystalline phases that

precipitated in the coatings during firing were related to

the color. A technique for producing uniquely light yet high


chroma colors through control of zircon precipitate particle

size was demonstrated.

In addition, a statistical model was developed for

calculating the coating melt viscosity as a function of the

frit oxide composition and temperature. Melt viscosity

versus temperature curves were applied to predict a frit's

potential for producing strong and stable color.



I.1 Color in the Ceramics Industry

The color of a product often determines its aesthetic

and monetary value. Selling prices of ceramics such as tile,

brick, artware, dinnerware, cookware, porcelain enamel,

concrete, bathroom fixtures and decorative glass are directly

related to their appearance.

Customers often select ceramic products based on viewinq

sample chips or prototypes at stores or retail distributors.

Sometimes buyers wish to color coordinate with the fixtures,

appliances or paint of an existing building. Occasionally,

customers purchase more of the same product in the future,

for example, adding the same color floor tile to an enlarged

room. In all of these cases, it is imperative that

manufacturers strictly conform to tight color tolerances,

year after year, in order for goods to comply visually with

customer expectations.

Inconsistencies in manufactured colors lead to

significant increases in industrial costs. Noticeable color


variations in fired coatings due to normal fluctuations in

manufacturing processing conditions result in nonstandard,

scrap products and lower productivity. For example, a major

portion of the $120 million worth of products scrapped in

1997 by U.S. ceramic tile manufacturers resulted from out-of-

tolerance colors. Since the U.S. ceramic tile market only

comprises about 0.6% of the world ceramic whitewares sector,

problems with color variations result in significant

industrial waste worldwide [Sez98] In addition, produce

inventory levels must be increased in order to accommodate

muiriole color shades per item.

Color consistency in manufacturing has become

increasingly difficult due to the rapid evolution of

processing technology to improve productivity and

profitability. Often during the transition, accessories for

the same product line must match in color but are made with

wo different processes. For example, in the ceramic tile

industry, flat "field" tile is predominately manufactured

with completely automated fast-fire roller kiln technology,

while difficult to handle trim and angle shapes are

constrained to high-labor slow-fire tunnel kiln processes.

Firina differences between the processes (30-minute fast-fire

vs. 14-hcur slow-f-ire cycles) complicate the formation of

matching glaze colors, but customers demand no noticeable

difference between coordinating trim and field glazes. Color

incompatibility between these products is currently the

largest customer complaint in the ceramic tile industry.

Other whitewares companies, including some manufacturers of

sanitaryware and dinnerware, are planning to convert to the

same fast-fire roller kiln technology and will encounter

similar problems with color variations.

Undesirable color differences between coatings batched

with the same formula occur even in facilities that utilize

the same type of firing technology throughout the factory.

Firing variations result from different kiln models, sizes

and shapes, the debugging of new kiln equipment, kiln fan and

burner wear over time, and changes in ambient conditions

which cause the kiln intake air density, humidity and

temperature to vary. Gaps in the product load entering a

kiln, normally due to breakdowns in machines upstream in the

production line, also cause firing temperature versus time

profiles to fluctuate. Shifts in firing conditions result in

variations in crystallization and pigment dissolution in

ceramic coatings, which alter their fired gloss, opacity and

color. This burdens industry with low yields, customer

complaints and potential loss of business.

Another source of color variation can be attributed to

the continued effort to reformulate ceramic coatings in order

to lower raw material costs. Unfortunately, some of the

cheaper systems have also yielded lower color strength and

stability during high-temperature processing. Due to

increasing foreign competition, domestic companies have been

compelled to lower manufacturing costs to enable selling

price reductions and gain a competitive edge. For example,

in the ceramic tile industry, import market share rose from

about 20% in the mid-1970s to over 60% in the 1990s [ Ear94].

Glaze raw material costs comprise roughly 10% of all tile

manufacturing expenses or approximately $100 million per year

[Fer96, Sez98] In order to stay in business, it is crucial

for whitewares companies to optimize color consistency while

minimizing glaze costs.

There is an increasing interest in the ceramics industry

to develop low cost color systems which are reproducible over

a range of processing conditions. High-temperature

interactions between multi-oxide glass frits and pigments in

ceramic glazes greatly affect the fired color. The influence

of frit is most significant since it is a relatively

expensive, carefully manufactured material usually added at

the highest weight percent of ingredients in fast-fire glaze

batches. Compared to other glaze components, frit normally

has the lowest melting temperature and is the most corrosive

to ceramic colorants. Most frit in the U.S. is used by

ceramic tile manufacturers, but frit consumption by other

whitewares industries will increase as they convert to fast-

fire roller kiln technology. Zircon doped pigments are the

most commonly used colorants for whitewares coatings because

they have the best high-temperature stability.

The overall objective of this research was to determine

the influence of various oxides in glass frits on color

development with zircon doped pigments during firing. The

results could be used to improve the color strength and

stability of industrial ceramic glaze systems.

This chapter very briefly introduces the reader to color

in ceramic glazes, the potential influence of frit on color

and an overview of the dissertation goals. More detailed

discussions are included in succeeding chapters.

1.2 Glaze Colorants

Ceramic glazes provide an impervious glassy decorative

coatinq for whitewares. Colors are produced with selective

scattering or absorption of incident light by colloidal-sized

particles suspended in the glassy matrix.

Solution colorants are sometimes introduced into the

glaze batch as oxides, then dissolved and precipitated as

metal ions during the firing process. Oxides such as Cr2O,

(green), CoO (blue), CuO (green to red), Fe203 (yellow to

brown) and MnO2 (purple to brown) were common sources of metal

ion solution colorants.

They are now rarely used in high volume whitewares

processes such as ceramic tile manufacturing because their

solubility and reprecipitation, and thus the color produced,

are extremely sensitive to the glaze composition, particle

size distribution, firing time and kiln atmosphere.

More typically, manufactured inert pigment particles are

added to glazes to obtain color. The most widely used for

industrial glazes are zircon crystal lattices doped with

metal ions. They provide a lower chroma than other pigments,

but the zircon structure is less soluble at high temperature.

Besides, most of the demand in the whitewares market is for

relatively weak, light colors.

The most common zircon-based pigments are zircon-

vanadium blue, zircon-iron coral and zircon-praseodymium

yellow. They are referred to as the triaxial pigments and

can be blended to achieve most glaze colors desired by

customers. Even though zircon crystals are more stable at

high temperature than other colorants, color variations still

occur. During firing, zircon may remain stable and protect

the metal ions, partially dissolve with that portion

reprecipitating or remaining in solution, or totally


Color control is further complicated because most

decorated ceramic whitewares contain multiple layers of

coatings. For example, a typical "stone look" floor tile

produced by Florida Tile Industries requires nine different

coatings over the pressed body (Table 1.1). Some

applications overlap, while others are distinctly separate on

the surface to create a more natural appearance and depth of

design. Both physical and chemical interactions between

layers influence pigment dissolution and the nucleation and

growth of new phases which affect opacity, gloss and color.

1.3 Potential Influence of Frit

Many variables influence color development in ceramic

glazes, as outlined in Table 1.2. The strength and high

temperature stability of ceramic pigments are highly

dependent upon the base glaze composition. Limited

preliminary studies [ Dec93, Byr94, Blo93] indicate that

Table 1.1. Example of Ceramic Coatings Applications on a
Decorated Floor Tile.

Application Application
Glaze Coating Color/Opacity Method Weight

(primer coat)


Middle coat


Ink 1

Ink 2

Ink 3

Ink 4






Light Grey/


Light Beige/



Rotating disk

Spray gun

Brushing machine

Rotating disk

Spray gun

Screen printer

Screen printer

Screen printer

Screen printer

Spray gun





<0 .001


0. 02

Table 1.2. Variables That Influence Ceramic Glaze Color.

I. Batch Composition

a. Base ingredients (oxide composition and phases
b. Pigments (composition, structure and loading)
c. Chemical additives (influence application drying
rate and smoothness)

II. Glaze Preparation with Ball Milling

a. Particle size distribution (influences melting

III. Application

a. Thickness (hiding power)
b. Drying rate (can affect composition gradient caused
by differences in particle settling rates)
c. Smoothness (influences gloss or degree of specular

IV Firing

a. Time vs. temperature (phase dissolution and
b. Kiln atmosphere (oxidation/reduction reactions,
sulfur "scumming," etc.)

improved slow-fire glaze compositions may reduce color

changes resulting from variations in glaze preparation,

application and firing conditions. However, there is no

published comprehensive or quantitative research on the

subject. There is also a great lack of research on fast-fire

glaze systems.

Frits are ceramic compositions that have been fused,

quenched to form a glass and granulated [ Dod94] They are

the primary ingredients in fast-fire ceramic glazes and in

most cases are the most reactive and corrosive part of the


Frits for whitewares coatings are classified as either

opaque (opacified; containing ZrO2) or transparent

(unopacified; no ZrO2), and glossy or matte. Besides ZrO2,

frits also normally employ SiO2 as the primary glass former,

alkalis (K20 and Na2C), B203 and ZnO or SrO as the main

fluxes, and other oxides such as CaO, Al203 and MgO. These

oxides are cost effective, environmentally safe and provide

the desired glaze properties. Compositions with BaO or PbO

are avoided because these elements are deemed hazardous by

the EPA. There is also an increasing interest in replacing

ZnO with SrO because ZnO is classified as a regulated

chemical by EPA. Sections 2.2.1-2.2.3 and 2.2.5 detail the

theoretical effects of individual frit oxides on the

properties of glasses and ceramic glazes.

High temperature properties of frits influence crystal

growth and dissolution rates in glazes. It was observed

[Jam85, Dor94] that dissolution and crystallization

velocities in multi-oxide glasses are diffusion transport

related and inversely proportional to the glass melt

viscosity, although no accurate models have been developed.

Glass viscosity, in turn, varies with composition and overall

has an Arrhenius-type inverse exponential relationship to

temperature. Phase changes in the glass resulting from these

phenomena alter the optical properties and color.

During fast-fire ceramic processing, a glaze is

typically in the molten stage at the peak temperature for

only 3 to 5 minutes. The rapid changes in heating and

cooling rates create a complex thermodynamic system where

phases are often not brought to equilibrium at high

temperature. Frit compositions which reduce the sensitivity

of crystallization and pigment dissolution to processing

variations would be beneficial for color control. The

"ideal" frit would preserve the pigment and precipitate the

same quantity and morphology of desired crystalline phases

over a wide range of firing conditions. The frit should also

produce a coating with enough opacity to hide the substrate

without significantly concealing the pigment and achieve the

desired surface gloss without defects. Currently, it is

not known if zircon pigments dissolve during fast-fire

cycles, and there is uncertainty regarding what phases


1.4 Overview of Dissertation Goals

The main goals of this investigation were to

1. Determine if glass frit oxide compositions could be

formulated to improve the fired color strength and high-

temperature stability of industrial whitewares coatings

colored with zircon pigments.

2. Relate the optical properties resulting from zircon-

vanadium pigment in a glass matrix to the color


3. Quantify the influence of individual frit oxides,

pigment loading and peak firing temperature on a

coating's color.

4. Correlate the evolution of the coating's structure and

properties to the original frit oxide composition and

the fired color.

5. Ascertain whether frit melt viscosity data can be

applied as an industrial quality control tool for

predicting a frits potential for producing strong and/or

stable color with zircon pigments.

"Fast-fire" ceramic tile manufacturing constitutes a

major portion of the whitewares industry and consumes most of

the frit produced in the U.S. This was the chosen processing

method for preparing and firing coating samples. Materials

selected for the study were eight laboratory-smelted frits

and a zircon-vanadium (Zr-V) blue pigment. Oxide

compositions of the frits were designed to provide cost

effective, environmentally safe formulas and comply with

Seger's rules (Section 2.2.2) for ensuring insolubility of

the frit and fired coating, and ready fusion at high

temperature. The range of oxide contents tested encompassed

and exceeded the range normally employed for glossy ceramic

tile glazes. Special emphasis was placed on comparing frit

compositions with ZrO2 (opacified) versus no ZrO2

(unopacified), SrO versus ZnO as the secondary flux, and

alkali/silica ratios. The B203 contents were kept low in

order to avoid liquid-liquid phase separation. The Zr-V

pigment tested was the blue colorant most commonly used in

the ceramic tile industry. The results will also be

applicable to other ceramic pigments which utilize the same

zircon structure to incorporate colorant metal ions.

Research goals were achieved by performing the following


1. Each of the eight experimental frits were loaded with

four different pigment concentrations of 0%, 0.5%, 2.0%

and 5.0% by weight. They were blended with water and a

suspending agent to produce 32 different glaze coatings.

2. Coatings were applied to opaque 2"X6" wall tile body

substrates using a wet spray method. Samples of each

formula were fired to 10000C, 10500C and 11000C peak

temperatures using a standard "fast-fire" ceramic tile

industrial heating profile. A total of 96 different

fired coatings were produced.

3. The spectral reflectance versus wavelength and the gloss

of each fired coating were measured. The CIE L* a* b*

color values, pigment absorption factors (K/S), and

color differences between tiles fired to 10500C and

1100'C (AE*) were calculated. Relationships between

light absorption by the pigment and color values based

on human perception were quantified.


4. Dilatometry and heating microscopy methods were employed

to measure the Tg, Ts and melt viscosity versus

temperature of coatings batched with 2.0% Zr-V.

5. In coatings batched with 2.0% Zr-V, phase changes and

resulting microstructures that formed during firing were

identified using x-ray diffraction, scanning electron

microscopy and energy dispersive x-ray spectroscopy

techniques. Fired coatings were quantitatively analyzed

for contents of Zr-V pigment and zircon which

precipitated from ZrO, and SiO2 in the frit.

6. Statistical models were derived to predict K/S and LE*

given the original frit oxide composition, pigment

loading and peak firing temperature. An equation was

also developed for calculating log 1] of the frit with

2.0% Zr-V given the frit oxide composition and


Color strength and stability were correlated to melt

viscosity, crystallization and Zr-V pigment


8. The mathematical models and experimental observations

were related to current scientific literature in order

to collate hypotheses which explain the results.

The foundation of materials science and engineering

research is to gain a better understanding of relationships

between processing, structure and properties of materials.

Figure 1.1 summarizes critical steps taken during this

research to define the processing-structure-properties

relationships of interest. This investigation focused mainly

on variables that influence a ceramic coating's color

strength and stability.

1.5 Guide for Using This Dissertation

The present document is greater in length than most

dissertations. The primary objective was not only to unveil

valuable information for basic science interests but also to

compile a text that could be used as a reference by engineers

working in industry. Thus, some sections may be bypassed if

only very specific information is desired.

In the Background chapter, Section 2.1 overviews current

scientific principles behind (a) materials interactions with

light with a focus on ceramics, (b) color perception by the

human eye and (c) the most common industrial method for

quantifying color and correlating it to human vision.

Section 2.2 summarizes current knowledge of the materials,

processing, structures and properties of ceramic whitewares


8 Glass Frits (oxide composition, density)

Zircon / Vanadium Blue Pigment


- Wet Mix 32 Formulas: 8 Frits X 4 Pigment Concentrations

Wet Applications of Coatings to Tile Substrates

Firing Temperatures: 1OQOC, 1050C, 11 OOC

96 Fired Coatings Produced

Figure 1.1. Flow chart summary of main research variables.






- Melt Viscosity: Heating Microscopy and Dilatometry

- Color Strength & Stability: Spectrophotometry &
L*a*b* Color System

Gloss: Gloss Meter

coatings and their influences on color. A special emphasis

is placed on ceramic tile glazes. A review of common frit

compositions, ceramic colorants, crystallization, phase

separation and melt viscosity relationships is given.

Throughout the Procedure, Results and Discussion

chapters, references are made to specific principles and

equations outlined in Chapter 2.

Chapter 3 details the experimental procedures applied

for the research. This includes descriptions of typical

industrial "fast-fire" ceramic glaze frit compositions, wet

coating application methods and firing profiles. The two

main categories of frits investigated were with and without

ZrO2. Materials characterization and analytical techniques

and procedures typically applied by industry to evaluate

whitewares coatings are also reviewed.

Chapter 4 shows the results of the research performed

for this dissertation. The particle size distributions,

densities and chemical analyses of the starting frits and

Zr-V blue pigment are given in Section 4.1. Section 4.2

details the optical properties of each of the 96 fired

coatings samples, as indicated by spectral reflectance

curves, gloss measurements and calculated color values of L*,

a*, b*, K/S and AE*0i1C50 I0oc* Section 4.3 reveals the

viscosity versus temperature profiles, heating microscope

images and dilatometric data for coatings loaded with 2.0%

Zr-V. Statistical models for predicting color strength

(K/S), color stability (AE*1050 1 00oC) and melt viscosity as a

function of the frit oxide composition and firing temperature

are given in Section 4.4. These equations provide a method

for engineers in the whitewares industry to estimate the

potential color strength, color stability and melt viscosity

resulting from various frit compositions when utilizing a

typical "fast-fire" heating profile. If the reader is only

interested in specifying frit compositions to obtain certain

color or viscosity results but is not concerned with the

crystallization or pigment dissolution processes responsible

for the optical properties, then it is not necessary to read

Sections 4.5 and 5.1.

Section 4.5 details the structures, compositions and

morphologies of crystalline species that precipitated in the

coatings during firing. An analysis for zircon present in

the coatings quantifies the amount of zircon precipitation

from fritted SiO2 and ZrO, and Zr-V pigment dissolution that

occurred during firing. Results from XRD, SEM and EDS

analyses are shown.

In Chapter 5, the Discussion, relationships are

established between color strength and stability, specific

oxides in the glass frit, Zr-V loading, crystallization, Zr-V

dissolution and melt viscosity. Scientific explanations for

observed phenomena are proposed. The Discussion focuses on

basic science interests, although Section 5.2.2 is also

noteworthy for engineers in industry. It correlates

important characteristics of a coating's log rj versus

temperature plot to the color strength and stability.


2.1 Color Theory

The color of an object is its most apparent attribute.

Other properties such as gloss and opacity also contribute to


Color is a term that can be used to describe the

reflection or transmission of light in visible wavelengths,

the properties of an object and the perception of the eye.

As one pioneer of color science, Dean B. Judd, stated


Color is that aspect of the appearance of objects
and lights which depends upon the spectral
composition of the radiant energy reaching the
retina of the eye and upon its temporal and spatial
distribution thereon. (p. 3)

Thus, in order to understand color, we must consider the

three elements involved with the production of color: the

light source,the physical modifications of light by matter

and the human eye as a color sensor. Various units typically

applied to quantify light and color are listed in Appendix A

along with essential conversion factors.


2.1.1 Liqht and the Visible Spectrum

Light is the visible radiant energy which interacts with

matter to produce what our eyes detect as color. It is an

electromagnetic wave that propagates as electric and magnetic

fields. Maxwell's theory [Hal86] predicted the existence of

a spectrum of electromagnetic waves differing only in

wavelength and traveling through space in a vacuum with a

speed of c = 3 x 108 m/s. Electromagnetic waves other than

light include radio waves, microwaves and x-rays.

The energy of a light wave is quantized into small

bundles called photons. According to Einstein, the energy

(E) of a photon is [Tip8O]
E = hf = h- (2.1)

where h = 6.63 x 30-34 J-sec is Planck's constant, f is its

frequency and the wavelength.

Other photonic relationships frequently applied are


E mc (2.2)
p : mc (2.3)

kp h (2.4)

where m is the mass of a particle and p is its momentum.

These equatio-ns allow *.s to contemplate a photon or light as


either a particle of energy E or a wave with a characteristic

frequency and wavelength.

The wave-particle duality of light can be described

mathematically by considering two harmonic waves with

slightly different frequencies which contain time and space

dependent components [Hum93]

TP = sin [ kx-(ot] (2.5)


TP2 = sin [ (k+Ak)x -(o)+Ao))t] (2.6)

2 t
where k the wave number (2.7
0=27f = angular frequency (2.8

Superposition of XV and V2 and considering sin a + sin
= 2cos(-P).sinx+p) yield a new wave [Hum93]:

T T, + 2 =

2 cos Ot xi sin (k + x L0 + lt (2.9)
2 2 2 2

In (2.9), if Awo= 0 and Ak = 0, a monochromatic wave results

of the form

= 2 sin (kx-ot) (2.10)

Equation (2.10) illustrates the wave characteristics of


If Aw andAk are very large, the cosine part of (2.9)

modulates the amplitude of the wave, resulting in a string of

wave packets. If many waves are considered with frequencies

ranging between c and Aw, one wave packet results and the

photon can be depicted as a particle. A better intuitive

understanding of materials interactions with light can be

achieved by noting light's wave and particle characteristics.

The color of light is related to its energy and thus its

frequency or wavelength. As shown on the electromagnetic

spectrum in Figure 2.1 [Hun87] visible light falls in a

range of 380 nm to 760 nm in wavelength. White light is

comprised of all the visible wavelengths.

Light can be produced by heating objects to

incandescence, or by exciting atoms or molecules with other

forms of energy.

Incandescent sources are applied to produce light with a

wavelength energy distribution similar to daylight (Figure

2.2) [Bil67] When a material is heated to incandescence,

the increased vibration of its atoms results in kinetic

energy that is sufficient to excite electrons to higher

energy levels. Photons are released when the electrons drop

back to their normal energy levels. As atom vibrations

become more energetic, the frequency and energy of emitted

tn16 In14 1n12 in10

-, ,u ... -o

10a to6 10~


300 4


....... ~LIGHT ".-..
I -I I II-
00 500 600 700 760 BROADCAST



,,, 1I I


,10 4 I 4
,o' o"1,,2 10'


Figure 2.1. Electromagnetic spectrum. [Adapted from Hun87]


I I I i li i I


i 0 I
i06 l08


b- -


I I I . . .

24 .22 .20 is,1




400 500 600 700
Wavelength, nm

Figure 2.2. Wavelength vs. energy distribution of daylight.
[Adapted from Bi167] (Note: Relative energy distribution
plots set the energy at 555 nm equal to 100, and the rest of
the curve is relative to the distribution radiated from the

light increases. The color of light produced changes from

red at low temperatures to nearly white at higher


The correlated color temperature of an incandescent

source is defined by the temperature at which a black body

would operate to produce a visual color match with the

incandescent source [Hun87]. The color of a real black body

depends only on its temperature, not its composition.

According to Wien's displacement law [Wea79] the product of

the absolute temperature of a radiating black body and the

wavelength corresponding to the maximum energy is a constant:

X: T = W (2.

where W Wien's displacement constant.

A common incandescent light source which operates at a

high enough temperature to emit a spectrum close to daylight

involves heating a tungsten filament enclosed in an evacuated

fused silica buln. Tungsten filaments are close

approximations to black bodies. Some tungsten filament lamps

used for light sources in color measurement devices

incorporate glass filters to provide a more accurate match to

the daylight spectral energy distribution.

Light can also be generated from luminescence or outer

electron shell interactions in fluorescent and phosphorescent

materials [Ask94] In luminescence, kinetic heat energy is

not essential for the mechanism of excitation. Luminescence

occurs when light has sufficient energy to excite valence

band electrons through the energy gap and into the conduction

band. When the electrons eventually fall back to the valence

band, photons are emitted. If the photon energy corresponds

to wavelengths between 380 nm-760 nm, visible light is

produced. In fluorescent materials, photon wavelengths can

be calculated with
E (2.12)

where Eg is the energy gap. Fluorescent lamps are

electrically excited to produce light. Normally with such

light, the spectral energy distribution is not as continuous

as with incandescent sources. Spectral lines are typically

narrow at specific wavelengths. In order to broaden the

spectral curve, sometimes more than one source is used in

combination. For example, in common household fluorescent

lamps, a spectrum from mercury vapor, electrically stimulated

inside the bulb, interacts with fluorescent powder on the

inside of the glass tube to generate a "cool white" light.

It is common to us- from one to several light sources acting

in combination as illuminates in color measurement devices

such as spectrophotometers [Bil67].

2.1.2 Materials Interactions with LiQht

Properties of a material that influence its appearance

include index of refraction, gloss, translucency,

reflectivity, transparency, absorption and color. These

properties result primarily from the interaction between

light and a material's electronic structure and

microstructure. When photons interact with a material, they

are either attenuated (reflected or absorbed) or transmitted.

As photons enter a material, their speed will also change,

resulting in refraction. Light may be partially reflected,

absorbed, or transmitted as related to the incoming beam

intensity [ io] by [ Ask94]

I = Ir + Ia + 1, (2.13

where Ir, IC and I, are portions of the incident beam that is

reflected, absorbed and transmitted, respectively. The

combination of wavelengths of light reflected from an

opaque material or reflected and/or transmitted from a

nonopaque material produce its color.

2.1.2a Refraction

The refraction of light by a material is estimated by

Snell's law [Che83]:
sin 0 n,
n i (2 .1 4 )
sin 0 n


0i = angle of incidence from the line normal to the

irradiated surface.

0- = angle of transmission from the same plane.

n, = index of refraction of material.

n. = index of refraction of medium.

n. relative index of Yefraction of material to


Normally, n is used as the notation for index of refraction

if the medium is air or a vacuum. Snell's law can be derived

from Fermat's principle [ Tip80] :

The paTri taken by light in traveling from one point
to another is such that the time of travel is a
minimum compared with nearby paths. (p. 612)

When light passes from air into a denser material, its

velocity decreases. Following Fermat's principle, liaht will

minimize its travel time by increasing its optical path

length in air relative to the path length in the denser

material. This results in a change in Qi, Ot and n. Thus, n

is related to the velocity and wavelength of light, which is

given by

n - =' 2.5

where u and Xmaterial are the velocity and wavelength of light

passing through a material and Xair is the wavelength of

incident light in air.

At a constant wavelength of incoming light, n tends to

increase for denser materials. When comparing values for

ceramic vs. polymeric (teflon and polystyrene) materials in

Table 2.1 [Wea79] it becomes evident that the structure of a

material also influences n.

If a material is easily polarized, there are increased

interactions of its electronic structure with incident

photons. In dielectrics such as ceramics, the index of

refraction is related to the relative dielectric constant

(K') by [ Kin76]

n = K' + K (2.16)

where Ki is the index of absorption.

Polarization (P) of the electron cloud around an atomic

nucleus is proportional to the electric field strength (E) of

the incoming light:

P = N 2 E


Table 2.1. Index of Refraction of Selected Materials
at 589 nm Wavelength in Air [Wea79].

Material Density Mean Refractive Index
(g/cm3) (n)

Water 1.0 1.33
Polystyrene 1.06 1.60
SiO2 (glass) 1.41-1.46 1.46

Teflon 2.17 1.35

Silicon 2.33 3.49

SiO2 (quartz) 2.64-2.66 1.55

CaCO 2.93 1.60

Diamond 3.51 2.41

(X A!903 3.97 1.77

Fe203 (hematite) 5.24 2.95

where a is the average dipole moment per unit field strength

or the polarizability and N is the number of material

particles per unit volume.

By the Lorentz-Lorentz equation, electronic polarization

is linked to the refractive index of a monatomic gas:
3 F_
n (2.18)
No n

where Eo is the dielectric constant in a vacuum, N. is

avagadro's number, and n_ is the molar refractivity. The

molar refractivity n_ is determined by measuring n at various

wavelengths of light as shown in Figure 2.3 and then

extrapolating to infinite wavelength.

Since the electron density is uniform within an atomic

radius (ro), polarizability is also related to the atomic

volume of a material:

X r (2.19)

Equation (2.19) shows that larger atoms, which contain more

electrons, exhibit greater polarizability and thus tend to

have a higher refractive index.

Ionic charge also plays an important role in influencing

the index of refraction. As the ionic charge becomes

increasingly negative, outer electrons are more loosely bound

and can increase& !olarizability. In addition, the refractive

index is dependent upon crystal structure symmetry, except in


Dense flint glass

1.60 Light flint glass
~Light flint glass

Booiiae glass


1.45 !!!
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Wavelength (microns)

Figure 2.3. Refractive index vs. wavelength of incident
light for three glasses. [Adapted from Kin76]

glasses and cubic crystals which are isotropic. Crystals

have a higher index of refraction in denser, close-packed

directions. For anisotropic substances, the mean index of

refraction is estimated as [Par73]

X+ + y(2.20)
n =
where X, P and y are refractive indices of the principle

crystallographic directions.

Multiphase crystalline and glassy substances have

specific refractive energies that are the sum of the

re.racrtve energies of their components [ Par73]:

Kr (2.21)


K, = k I00+ k p I00 +
10 0 100


K_ = specific refractive energy of a


n mean index of refraction of a substance.

p = density of a substance.

ki, k2 : specific refractive energies of the


PI, P2 weight percentages of the components.

Reference values for specific refractive energies of oxides

can be used to estimate the refractive indices of glasses,

glazes and crystalline species.

2.1.2b Surface Reflection and Gloss

When a beam of light strikes a material, a portion of

the photons may be reflected. The light reflected at an

angle equal to the incident angle is referred to as specular

reflection (Figure 2.4). This "mirror-like" scattering

occurs at one angle from the point of reflection on a smooth,

nonmetallic surface. If the surface has some roughness, some

light may be scattered at all angles from the point of

reflection. This diffuse reflection is common in ceramics

where surfaces are not normally perfectly smooth. The total

reflectivity is the fraction of incident light specularly and

diffusely reflected. The gloss of a surface is related to

the relative amounts of specular and diffuse reflections. It

can be defined as the degree of approach to a mirror surface.

A perfect mirror surface has a maximum gloss and reflects all

visible light. This surface itself is invisible and has no

apparent microstructure.

Within the visible spectrum, the reflectivity (R) from a

perfectly smooth surface in an air medium is the fraction of

Incident beam




Figure 2.4. Reflection and transmission of light by a glassy
material containing suspended particles. [Adapted from

incident light reflected at an angle equal to the incident

angle. This fraction of specular reflectance from normal

incidence (Oi=0) is calculated for the optical region of the

spectrum with Fresnel's formula [ Kin76:

{n-i l: (2.23
R (n+1j

Equation (2.22) shows that materials with a high index of

refraction have a high reflectivity. Since the index of

refraction varies with the wavelength of light, so does R.

From Fresnel's law, equations can be written to compare

the reflectJivity of plane polarized light so oriented to a

plane mirror surface that its reflection (ratio of reflected

to incident flux) is most facilitated (R ) or most hindered

(R,) in an air medium [ Jud65]:

cosO, n sin (2.24)

cos01+ n2 si


n cos 01 n sin 0i (2.25)

n cos i+ n sin 0,

where 0i is the angle of incidence.

For unpolarized incident light, the total reflectivity

(RT) is the average of R and

RT= (R 1 + R) / 2 (2.26)

Thus, the reflectivity, RT, for unpolarized light is the

average of reflectivities for plane polarized light in (RP

and perpendicular to (R.) the plane of the incident beam. If

0i = O', the incident beam is perpendicular to the surface and

perfect mirror specular reflection results. In this case,

equations (2.24) and (2.25) reduce to equation (2.23) (R -

R). If 0i = 900, only grazing incidence occurs and R R1

RT = 1. Between perpendicular and grazing incidence, R ,R

and RT vary.

For a perfect mirror surface R = R = RT = 1.0

regardless of Oi. For real colorant layers with a glossy

medium, mirror reflectance approaches unity with grazing

incidence as 0i -- 90'. In this case, the incident beam

contacts only that part of the colorant layer which is just

below the surface. This is the high-gloss transparent medium

carrying suspended pigment particles.

Figure 2.5(a) shows the relationship between R R and

RT for 0i from 50 to 90' for an air/glass boundary where the

refractive index of the glass is 1.5. Figure 2.5(b) plots

total reflectivity as a function of 0i and index of

refraction. Figure. 5 can be used to estimate the gloss or


0.10 1.0

0.09 n2zn1=l.5 0.9

0.08 0.8

0.07 0.7

0.06- 0.6

0.05 0.5
0.03 0.3

0.02 0.2

0.0 -0.1

10 20 30* 40 50' 60" 70 80* 90.


0.10 1.0
0.09 0.9

0.08 -0.8

0.07 -0.7

0.06 0.6


ko 0.04 -0.4

0.03 0.3

0.02 0.2


10' 20' 30' 40' 50" 60' 70' 80 90*


Figure 2.5. Fresnel reflection for a) an air/glass boundary
and b) total reflectivity for different index of refraction

degree of approach to a mirror surface for mediums such as

plastics, glass, textile fibers and paint vehicles [ Jud65].

Note in Figure 2.5(a) that for a smooth glass with n =

1.5, R -- 0 at 0, = 56'. This follows Brewster's law, which

states that mirror reflectance is most facilitated (R = 0)

when [ Jud65]

tan 0i = n (2.27)

Thus, for a glass of n = 1.5 at incident and viewing angles

of approximately 560, there is a lack of polarized diffusely

reflected iaght. Parallel polarized light in the reflected

beam is the only component present from the unpolarized

incident light. This principle has been applied to measure

gloss through the use of a polarizing element which subtracts

the specular component at Brewster's angle where R, = 0.

Brewster's law is also employed to measure the index of

refraction of smooth glass [ Fle93] A light polarizer and

detector are used to measure the polarization effectiveness

of light reflecting from the glass surface. The angle of

incidence (0k) where reflected polarization is most efficient

is applied to calculate n with equation (2.27).

As the surface roughness of an opaque coating or a glass

matrix with suspended colDrant particles a greater

portion of the reflection becomes diffuse. This broadening

of the reflection band and lowering of the specular intensity

tends to lower the gloss. Gloss is greater for smoother,

higher index of refraction surfaces. Surface roughness in

ceramic glazes caused by crystal structures, defects,

interfaces, or a uneven application usually lowers the gloss

by increasing the amount of diffuse reflection.

The relative amounts of specular and diffuse reflection,

and the gloss of the material, have an effect on the color

revealed. For example, glossy paint will appear to lose its

color in daylight glare, but "flat" paint will look nearly

the same. Most color measurement devices take reflection and

gloss into account when generating values for color.

2.1.2c Opacity and Translucency

Subsurface reflections can occur in materials that are

not completely opaque. The reflectivity of opaque metals is

typically 0.9 to 0.95, where most clear glasses are closer to

0.05 [Ask94] .

Optical characteristics of ceramic glazes, glasses and

enamels can be developed by modifying their internal

reflective and light-scattering properties. Characteristics

such as the portion of light specularly reflected (gloss),

the portion of light diffusely reflected (opacity), and the

portions of light directly and diffusely transmitted are

important (Figure 2.4). These attributes are influenced by

the light-scattering properties of phases or small opacifying

particles suspended in the glassy matrix. Good opacification

is obtained with the high light scattering and reflectivity

this mechanism provides.

Common opacifiers used in ceramics coatings include

zircon (ZrO .SiO zirconia (ZrO), SnO2, TiO, and Al20

They are selected based on their optical properties, the

desired coating composition, processing limitations and

properties that affect compatibility with the matrix phase

such as thermal expansion, solubility, hardness and melting


Opacifiers can be inert with respect to the host matrix

phase, formed during melting, or crystallized from the glass

melt. Very fine particles can be obtained from materials

such as TiO, or at higher firing temperatures ZrO2, which can

be melted, nucleated and re-crystallized during the heating


The degree of opacity of ceramics which contain

particles suspended in a glassy matrix depends on five main

factors [ Par73]:

1. The difference in refractive index between the matrix

and dispersed particles. This effect is described by

(n n )
S= Io (2.28)
(n + nJ2


Ir = intensity of diffuse reflected light or intensity

of opacification.

I0 = incident beam intensity.

ni = index of refraction of the glassy matrix.

n2 = index of refraction of the opacifier.

In ceramic coatings, this mechanism provides the

greatest influence on opacity. As the difference between the

refractive indices of the matrix and particle phases

increases, more light scattering and higher opacification is

achieved. Gencrayv, glazes and enamels have refractive

indices ranging from 1.50 to 1.70 while opacifiers range from

2.0 to 2.8 (Table 2.2) [1 Ree83] .

2. The size of dispersed particles which scatter light.

The light-scattering ability of an optically

heterogeneous material can be estimated with the scattering

or turbidity coefricient (S). This coefficient is a

Table 2.2. Properties of Materials Used
Ceramic Glazes [Par73].

Opacifier Mean Index ot Difference in n:
Material Refraction Opacifier-Glaze

TiO2 2.50 0.95

ZrO2 2.40 0.85

ZrO 2SiO2 2.05 0.50

SnO2 2.04 0.49

Air i.00 0.55


for Opacifying





1, 625

of Expansion


4 1



measurement of the attenuation due to scattering of light as

it traverses a medium containing scattering particles

[ Kin76]
S S V r (2.29)
4 fp


exp -IV 4r exp(-Sx) (2.30)


Sf = scattering factor that varies between 0 and 4.

S= volume fraction of scattering particles.

r = radius of the scattering particle.

I iIc =ratio of light intensity scattered/initial


x = optical path length.

Equation (2.29, shows that scattering, and thus opacity,

tends to increase up to a point with decreasing particle

size. The scattering constant (Sf) increases with particle

size (r) and is inversely proportional to the fourth power of

wavelength for particle sizes much smaller than the

wavelength of incident light. When the particle size is

approximately equal to the wavelength of light, Sf reaches its

maximum value, then decreases with increasing particle size.

Thus, maximum scattering occurs when the opacifier has a

particle size similar to the wavelength of light used, which

is in the range of 0.38 to 0.76 microns in diameter for

visible light.

3. The number of reflecting particles per unit volume.

Equations (2.29) and (2.30) indicate that opacity

increases with the number of particles. As the concentration

of opacifier increases, the rate of increase of opacity

decreases. Glazes and enamels typically utilize a maximum of

17% zircon by weight for opacification. Approximately 3% to

4% becomes an intermediate part of the amorphous glass

structure, while the rest serves as light-scattering


4. Higher opacification is obtained when there is a

distinct boundary and steep concentration gradient

between the matrix and particle phases.

Diffusion and the consequent reduction in concentration

gradient between the matrix and particles results in lower

opacification. Opacifier/glass systems with relatively low

diffusion coefficients at the required processing

temperatures are most effective. Crystals precipitated in a

glass during the heating or cooling cycle tend to have sharp

interface boundaries.

5. The thickness of a coating applied to a substrate.

Coating thickness effects on covering power can be

related with the Kubelka and Munk equations [ Kin76]:

(1/R_)(R'-R_) R RR-I-exp Sx --R_.

(R' -RJ- RI exp Sx(1 RJ

K K 2K
R =1+ + (2. 32


RR, coating reflectance.

R'= substrate reflectance.

R-= total reflectivity of a colorant layer so thick

that further increases in layer thickness do not

change the reflectivity.

S = scattering coefficient

K = absorption coefficient.

x = coating thickness.

Equation (2.31) shows that coating reflectance increases

up to a point with thicker applications and higher reflection

substrates. Figure 2.6 demonstrates the increase in

reflectance with application thickness of a typical TiO,

opacified white glaze fired to 1000'C. The main

disadvantages of a thicker coating is the increased material

requirements and cost.

Equations (2.31) and (2.32) indicate that opacifiers

with a high scattering coefficient (S) and low absorption

coefficient (K) are most powerful. The quantity Sx is often

applied to estimate the scattering power of a coating.

Another method gauges opacity with the ratio of reflectance

obtained from a coating over a black (R' = 0) versus a white

(R' = 0.89' backing. This is the Tappi Opacity Method for

determining the contrast ratio C0.9 = R'0/RI0.89.

Liquid-liquid phase separation during glass formation is

another method by which glaze opacification can occur. For

example, the Li20 SiO, Ti02 system separates at high

temperature into a low refractive index silicate glass and a

high index titania rich glass [Kim59] One disadvantage of

this mechanism is that it is very sensitive to processing

temperature. Therefore, in current manufacturing settings

where heating variations during firing are common, the

100 1

90 30 ,,

80Z N

70 1






400 450 500 550 600 650 700
Wavelength, millimicrons

Figure 2.6. Reflectance vs. wavelength of light for a Ti02
opacified white glaze fired to 1000C, at various glaze
application weights in g/ft2. [Adapted from 2ar731

relative proportions of glassy phases and opacification would

be inconsistent and cause product appearance variations.

If translucent rather than opacified appearances are

desired, particles in tne glassy phase must create diffuse

transmission. Translucency is important for products such as

opal glass, where opaque substrates are not utilized. It is

most common to achieve translucency by dispersing a

particulate phase with a slightly different index of

refraction than the glassy matrix. Translucency is also

often controlled with porosity, where lower pore

concentrations (higher material density) or higher pore size

at a given concentration increase translucency.

2.!.2d Absorption, Transmission and Color

Light that is not reflected or transmitted by a material

is absorbed. The linear absorption coefficient (K) indicates

the portion of normally incident radiant energy absorbed

through a unit distance (x) in a single phase material by

T t exp(-Kx) (2.33)


T : fraction of light transmitted as it passes through

a material.

It/Ii = transmitted intensity of light/initial intensity

of beam after reflection.

In the Raleigh scattering mechanism of absorption,

photons are deflected from electrons orbiting an atom without

any change in energy. This mechanism is more common for high

atomic number atoms and low photon energies [Ask94]. If an

electron is ejected from an atom, consuming some of the

photon energy, this is referred to as Compton scattering.

Resonance occurs when the frequency of material oscillations

is close to the frequency of incident radiation, which

results in the absorption of radiation.

If incident light stimulates electrons to change their

energy level, the photons are absorbed and the material is

opaque to this particular wavelength of light. Because there

is no energy gap in metals, electron movement into higher

energy levels occurs at almost any photon energy. Therefore,

metals have a high absorption coefficient and are opaque to

most wavelengths of electromagnetic radiation.

The energy gap in semiconductors is greater than metals

and smaller than insulators. Semiconductors with small band

gaps can transmit photons with energies below the energy gap

Eg or become opaque and absorb photons of higher energy. For

example, at 300 K, Si has a gap energy of 1.12 eV, while

diamond has a gap energy of 5.47 eV [Hum93]. Therefore,

silicon requires less energy for electron transitions and

appears opaque in daylight, while pure diamond is

transparent. In the visible spectrum, Eg ? 3.1 eV materials

do not absorb any photons, where Eg 1.8 eV materials absorb

all visible light [Ask94]. For intermediate energy gaps, a

fraction of the incident visible light is absorbed.

In ionic ceramics, filled shells of tightly bound

electrons do not have energy levels available for electron

movement [Ric92], and most single crystals are transparent.

Covalent ceramics, however, vary in the level of absorption.

For example, diamond and graphite both have covalently bonded

carbon atoms, but their optical properties are significantly

different. Diamond is transparent while graphite appears

black. Although there is a strong covalent bonding within

the graphite hexagonal network, weak Vander Waal's bonding

between the layers allows for electron movement. This

results in electron transitions and absorption of visible

light. Good insulators with a large Eg such as diamond tend

to transmit light.

Absorption due to electron transitions and resonance is

intrinsic, while extrinsic effects in ceramics can also cause

absorption and color. Extrinsic effects include grain

boundaries, pores, inclusions, anisotropy and atom vacancies.

In ceramics, the absorption coefficient (K) is related

to the index of absorption (ki) (also referred to as the

attenuation index or extinction coefficient) by [Kin76]

K = 4nki/ (2.34)

From equations (2.15), (2.16) and (2.34), K increases with ki

and the index of refraction of a ceramic material and

decreases with higher wavelengths of incident light.

The overall fraction of light transmitted (T') after

both reflectance and absorption losses is

T (I- R) exp (-Kx)) (2.35)

where R is the reflectivity and It/IO is the ratio of

transmitted to incident light intensities. By equations

(2.13), (2.23), (2.28) and (2.35), all of the incoming light

can be accounted for by reflection, absorption and


Total light interaction with a material can thus be

written [Ask94]
Irf IR (2.36)

I a = (iIIf)- [I(l-R) exp(-Kx} ] (2.37)

In, = I R(I-R) exp(-Kx) (2.38)


I, = Io(l-R) exp(-Kx) (2.39)

= Ir + Ia + Ir, + I, (2.40)


Irf = intensity of light reflected at the incident


Ia = intensity of light absorbed by the material.

Irb = intensity of light reflected at the back face.

Color is produced in many materials through selective

scattering and absorption of incident light. This

selectivity often results from variations in the absorption

coefficient with wavelength. Four electron transitions

concurrent with this type of absorption are common causes of

color [Ric92]:

1. Internal transitions with rare-earth or transition

metals or other ions with incomplete inner electron


2. Charge transfer, where electrons are transferred

from one ion to another.

3. Electronic transition caused by crystal


4. Bad gap transitions found in many semiconducting

compounds, as discussed earlier in this section.

Transitions (1), (2) and (3) usually are caused by impurities

or defects in a material, while (4) is a bulk property.

Often, particles are suspended in a matrix such as a glass to

create electronic transitions and color. The absorption

coefficient is proportional to the concentration of absorbing

ion (c), according to Beer's law [Ree83]:

T = exp (-Ecx) (2.41)
K = cc (2.42)

where E is the extinction coefficient observed per unit

concentration. This is the fundamental law of simple

subtractive colorant mixing.

The most commonly used colorant ions are from transition

metal compounds or impurities such as V, Cr, Mn, Fe, Co, Ni

and Cu shown in Table 2.3 [Ree83]. They provide color in

many ceramic bodies, glazes, glasses, minerals, gems,

pigments and paints.

Crystal or ligand field theories describe how these

elements produce color [ Pet72] Transition metals have

unfilled inner orbitals available for the creation of split

energy levels for electronic transitions. In "free" ions,

orbitals have equal energies but different spatial

orientations, as shown in Figure 2.7 for the five d orbitals.

But the coordination of negatively charged anions about the

A .f -

~.. ;.~


Figure 2.7. The 5 d orbitals. [Adapted from Kin76]

Table 2.3. Transition Elements and Their Properties [ Pet72].

V Cr Mn Fe Co Ni Cu
Atomic number 23 24 25 26 27 28 29
Atomic Radius, 1.31 1.25 1.37 1.24 1.25 1.25 1.28
Electronic 3dS4s2 3d54s' 3d54s2 3d64s2 3,74s2 3d84s2 3d104.3
First 155 156 171 182 181 176
Second 338 334 361 373 393 418
Third 676 713 777 706 772 810
Oxidation +1.2 +0.91 +1.18 +0.44 +0.28 +0.25 -0.34
Oxidation 2,3,4,5 2,3,6 2,3,4,7 2,3 2,3 2 1,2
Melting point, 1710 1930 1220 1535 1495 1455 1083

Density, g/cc 5.96 7.20 7.20 7.86 8.9 8.90 8.92

Hardness5 9.0 5.0 4.5 2.5-3.0

Electrical --- 62 32 16 17 24 96
lEach atom has an argon inner core configuration.
2Values are in kcal/mole.
3For the oxidation process: M(s) = M2+(aq) + 2e-.
4Common oxidation states; the most stable one is italic.
5Hardness values are on the Mohs scale.
6Compared to an arbitrarily assigned value of 100 for silver.

metal cation produces an electrostatic field that raises

inner orbital energies nonuniformly. This electrostatic

interaction between anions and metal ion's electron clouds

splits inner d or f oroitals into different energy levels.

The energy and corresponding wavelength of light absorbed by

the metal which produces color is equal to the difference in

the split energy levels.

For example, in a tetrahedral structure surrounding a

metal ion with unfilled d orbitals, the df dx and d...

orbitals have more energy than the d-_y- and d,- orbitals.

Color-producing transitions are allowed between these two

split groups, and the wavelengths of light absorbed depend

upon the magnitude of the splitting. Thus, only a limited

range of colors can be produced by any given ion.

The oxidation state of the metal also has an influence

on the magnitude of splitting and resulting spectral

properties. For example, Cu is colorless in solution while

Cu+2 has a strong blue color [ Pot67] When the valence of a

given element increases (e.g., smaller d occupancy), so does

the strength of the ligand field.

This section reviewed the most common causes of color in

materials and the method by which color will be derived

during the subsequent research involved with this

dissertation. A comprehensive list of all of the possible

causes of color are listed in Appendix B.

2.1.3 Color Perception by the Human Eye

The eye is the human optical system (Figure 2.8) [ Tip80]

that allows us to perceive the color, gloss, opacity and

dimensions of an object. The eye is sensitive to light

between wavelengths of 400 and 700 nanometers.

Light enters the eye through the pupil and is focused by

the cornea-lens system on the retina. As the distance of an

object from the eye varies, the ciliary muscle changes the

lens shape to improve focus of the image on the retina.

The photosensitive parts of the eye are the rods and

cones of the retina. These tiny structures receive images

and transmit information along the optic nerve to the brain.

The size of an image on the retina increases with the number

of rods and cones activated, which is proportional to the

apparent size cf the object being viewed.

Rods respond to very small amounts of radiant energy

and, thus, serve for night vision. Rods do not detect hue or

chromatic colors but only perceive neutral colors such as

white, gray and black.


Central retinal
artery and vein

Figure 2.8. Human optical system. [Adapted from Tip80]

On the other hand, cones sense chromatic as well as

neutral colors. Cones, which are responsible for day vision,

can detect a much higher density of radiant flux than rods

but are less sensitive at very low levels of light. Rods

respond to minute quantities of light as low as 10-6 candelas

per square meter (cd/m2), while cones require at least 10-3

cd/m2 [ Jud65] .

At illumination commonly referred to as twilight, both

rods and cones are active. The approximate range of

luminances which correspond to twilight or the mesopic region

is from l0- cd/in2 to 10 cd/M2 [ Jud65] In this range, color

judgments are extremely unreliable because the relative

degree of rod and cone vision continually changes.

Therefore, color inspections in manufacturing should not be

carried out in this condition, although many factories and

industrial inspection areas are dimly lit. Luminance at

approximately 10' cd!m" is the maximum level where the human

eye can perceive color with cone vision.

The eye is not equally sensitive to all wavelengths of

light. It has been demonstrated that 555 nm light is viewed

more easily than other wavelengths. Figure 2.9 graphically

shows the sensitivity or relative response of the human eye

at daytime (cone or photopic curve) and nighttime (rod or



Ii .

,-J.. /\

I-. /
,,.,, //

0 .
400 500 600 700

Figure 2.9. Luminosity functions of the rods (nighttime
scotopic vision) and cones (daytime photopic vision) of the
human eye. (Adapted from Hun87]

scotopic curve) for the same amount of energy at different

wavelengths of light in the visible spectrum. The curves

were developed from experiments where 52 human observers

adjusted the intensity of light at different wavelengths

until they appeared equally luminous or bright [Hun87] The

property of light by which we define how easily we can see it

is referred to as luminosity.

Both the Young-Helmholtz and Hering experiments of the

mid-1800s confirmed that human observers see colors with

three spectrally unique receptors which detect black-white,

red-green and yellow-blue. Subsequent numeric scales

developed for quantifying color contain three values; one for

each opponent-color pair.

Color sensory responses of the eye are not linear with

the amount of stimulus. For example, there is a logarithmic

relationship between the actual light level reflected from an

object and its perceived lightness. Color perception is also

a function of the light source and directions of illumination

and view. For these reasons standardized observation

conditions are required for industrial inspection. Even so,

differences between individuals are great enough to affect

visual color quality control. Most often, human observations

are coupled with color measurements performed by machines

such as spectrophotometers in order to make final


2.1.4 Color Measurement

Color measurement, like human eye perception, depends on

the light source, the sample being viewed and the observing

apparatus. Properly operated color measurement equipment,

however, can provide more repeatable results than subjective

human perception. Through a series of calculations, measured

colorimetric data can be converted into values that better

relate to human vision.

2.1.4a Spectrophotometry

The spectral characteristics of an object determine its

perceived color. Spectral characteristics are defined by the

reflectance or transmittance of light from a material as a

function of its wavelength. Spectrophotometers are used to

measure reflectance or transmittance from a sample as a

percentage of incident light at each wavelength in the

visible spectrum, normally in 0.5 nm increments [Mac9la].

Typically, reflectance is measured for opaque materials and

transmittance for transparent materials where the color of

light after it passes through a material is important.

Figure 2.10 reveals reflectance curves for opaque

coatings colored with pigments which absorb a portion of the

incident light [Hun87] The white coating reflects a high

portion of the incident light across the whole visible

spectrum while the black coating absorbs most of the light

flux over the wavelength range. Colors of blue, green,

yellow and red are created through selective absorption and

reflection of different light wavelengths by the pigment.

For example, the blue coating is shown to absorb primarily

yellow to red light (550-700 nm) while reflecting blue (450-

550 nm). The color of a ceramic whiteware glaze coating

results from this mechanism. Glazes are applied over an

opaque white substrate, and the reflectance curve produced is

the sum of reflectances from the pigment particles, other

crystalline species present, and the white substrate minus

specific wavelengths of light absorbed by the pigment

colorant. Normally, the background substrate and undoped

pigment crystal strongly reflect all visible wavelengths and

appear white or light yellow without the light absorbing

metal ion incorporated in the pigment. In contrast, the

color of light transmitted through a nonopaque glass results

from the incident beam minus both light absorbed by the

structure and reflected from the irradiated side.




Figure 2.10. Reflectance versus wavelength for opaque
coatings colored with pigments that absorb a portion of
incident light. [Adapted from Hun87].

The basic components of spectrophotometers are outlined

in Figure 2.11. Reflectance factors are measured one

wavelength at a time, normally at 0.5 nm increments, by

isolating wavelengths with gratings, prisms or interference

filters and slits. This is the monochromator device in

Figure 2.11 [Hun87] Current spectrophotometers are similar

to original mechanism developed by A. C. Hardy in 1928, shown

in Figure 2.12. The position of mirror slit #2 is adjusted

for wavelength isolation.

Typical light sources include a tungsten filament lamp

or a pulsed xenon bulb, which, in conjunction with a prism,

produce white light. Illumination is normally near 10' cd/mr

where only cone vision occurs. For accurate color

comparisons, the relative energy versus wavelength

distribution from the source must exactly match the desired

standard, but the total energy or illuminance from the source

can range from 10 cd,/n2 to 106 cd/i2 where the rods are


Real liQht sources are difficult to standardize, and it

is often useful to compare the color of objects viewed under

various wavelength energy distributions. Normally

reflectance values from the real light source are



-~ \-


Figure 2.11. Basic components of spectrophotometers.
[ Adapted from Hun87]

W atee n g t S p e c u l a r
Apertre po.ailfng rau lSa nd
Lens Aperturt Slit #e r filter t

Collimator PDom#1codeset
enI N Lamm
Photometer #2m Sev motor I s ..le

Photometer caNOTEgls o
sc~~D aleh motor srophttue

~ du amplifier aelctdud

Figure 2.12. Schematic of the Hardy spectrophotometer.
Adapted from Bi167]

mathematically converted to represent theoretical sources or

illuminants before color values are derived. Outputs from

spectrophotometric measurements include color values derived

from relative energy distributions of standard light sources

such as D65 (average noon daylight from the total sky),

illuminant A (incandescent lamp), illuminant B (near

sunlight) and illuminant C (average daylight from the total


The standard full visual field of view utilized to

detect light reflecting from an object is 2' angular

subtense. Occasionally, a 100 observer is used to provide a

larger field of view.

Light flux reflected from a sample is collected for

measurement by a white-lined integrating sphere. Elimination

of surface gloss from the color measurement provides results

which better correlate to visual inspection. This can be

accomplished by replacing the white plug on the sphere's

specular cup with a black plug. Since the specular cup is

offset to be illuminated at an angle of reflection equal to

the angle of the incident beam, the black plug absorbs

primarily specularly reflected light. Diffusely reflected

flux is diverted up the sphere to the photodetector. The

collected photon energy distribution is converted into an

electrical signal and sent to a computer. The computer

program converts measured spectral data into numbers that can

be more easily interpreted and correlated to the response of

the human eye.

Measurements of gloss can be performed separately with

goniophotometers or gloss meters, which measure the spectral

reflectance or quantity of light emitted in directions

related to the surface characteristics of the object. The

gloss of ceramic coatings is normally measured at a 600 angle

of incidence, where mirror reflectance is most facilitated,

according to Brewster's law (equation 2.27).

2.1.4b Basis for Color -uantification

The average sensitivity of the human eye to each

wavelength of light has been determined through extensive

experimentation [ Bil67, Hun87, Jud65, MacA35, MacA42] Human

observers were asked to visually match the colors of light

from individual wavelengths by mixing together lights from

three colored primaries. Three primaries were applied

because the eye contains three spectrally unique receptors

for detecting colors. The amounts of energy of each of the

three lights required to match single wavelength colors were

used to develop standard observer functions for the basis of

all color measurement. These weighting functions are applied

to transform spectrophotometric data into numbers that better

correlate to the way the human eye perceives colors.

The weighting functions ( x y and z ) are plotted in

Figure 2.13. Mathematical functions for describing colors

obtained by mixing different sets of primary colors have been

shown to always be related by a set of linear transformations

[Hun87] Therefore, there was some flexibility for selecting

the three standard primaries which providex y and z

the most user-friendly set of weighting functions. The

curves in Figure 2.13 were derived with the following useful


1. One of the functions, the y curve, was made to equal

the photopic plot shown previously in Figure 2.9, which

indicates the eye's response to luminosity or color


2. The areas underneath the three curves were made equal

for light of equal energy at all wavelengths.

3. One function was selected to be as near to zero as

possible for as much of the spectrum as possible.

In this form x y and z do not represent any real

colored primaries but can be converted to values that are






w T
> 100


50 _

400 500 600 700

Figure 2.13. Weighting functions used for the standard
observer at a 20 field of view. [Adapted from Bi167]

easier to apply. The weighting functions are used to

transform spectral reflectance curves into three numbers

referred to as tristimulus values, X, Y and Z. These values

specify color in terms of the mixture of red (X), green (Y)

and blue (Z) primary light that would produce the same color.

The Y value also still includes brightness detected. If two

materials are found to have the same measured X, Y and Z,

they will appear to have the same color under that specific

viewing condition.

At any one wavelength, X = x, Y = y and Z = z. For

example, at a wavelength of 450 nm in Figure 2.13, the light

detected would consist of proportions 32 : 5 : 175 of red ( x

or X) : green (y or Y) : blue (z or Z) light. For all

wavelengths in the visible spectrum, the contribution of each

tristimulus value can be calculated with [ Hun87]

X = Sk x + S XX + S) X + ... + S? X, (2.43)

X f f S. x dA (2.44)

x. = weighting function (x) value at X wavelength.

SX= spectral energy at ? wavelength.

Y (y) and Z ( z ) can be calculated in the same manner as X

x) with (2.43) and 2.44). The spectral energy, in turn, is

a function of the properties of the light source for an

illuminate or aperture color (SXsource) or the reflectance from

a reflecting object (S~materiaI) :

S source :E (2.45)


SmateriaI EX Rx (2.46)


EX = energy of the light source at ). wavelength.

RX = percent reflectance of light of ? wavelength from

the material.

Since objects are viewed in relation to their surroundings,

X, Y and Z are normally expressed relative to the luminosity

of a perfect white opaque material where R = 100, as

fE R x d%.
X = 100 f X (2.47)
f E y Ldk

f ER z ydX
Z 100 f (2.49'
E y dk

Thus, for a perfectly white material, Y is 100 and X and Z

vary depending upon the light source.

Trichromatic coefficients (x, y, z) are often calculated

from tristimulus values:

x (2.50)
x + Y + z

Y (2.51)
y x + Y + z

z (2. 52
x + Y + z

where x + y + z = 1.0. The x and y are coefficients used to

indicate chromaticity or color, while tristimulus Y is

normally kept to represent luminosity. MacAdam in 1935

[MacA35] proposed the first color measurement space with Y,

x, y cartesian coordinates.

Most current color measurement systems apply tristimulus

values rather than trichromatic coefficients. Tristimulus

values are further converted to allow for easier

interpretation of color in three-dimensional black-white,

red-green and yellow-blue space. Since the tristimulus

system was sanctioned by the International Commission on

Illumination or CIE in 1931, there have been over 30 three-

dimensional color spaces developed through transformations of

X, Y and Z values. The best scales provide an approximately

uniform color space where equal distances within the space

represent nearly equal visual color differences. The

current most commonly used color space in the world is the

CIE L*a*b* scale which was developed in 1976 (Mac96].

2.1.4c CIE L*a*b* Color Measurement Scale

Tristimulus data are converted into scales which, based

on visual discrimination experiments, correlate to perceived

color differences. Approximately uniform scales have been

developed where differences between measured colors

throughout the color space are proportional to visual


Human eye sensitivity for detecting color differences

varies across the visible spectrum of wavelengths observed.

Visual color discrimination is greatest near 485 nm and 590

nrm and least around 425 nm and 650 nm. This is represented

in the MacAdam color limits (Y, x, y) diagram in Figure

2.14). The greater the distance between two wavelengths on

the perimeter of the plot, the greater the range of colors

that can be perceived in the interval. The third dimension

indicated in the graph is the Y-value from 0 through 95.

Note as the Y-value or lightness increases, the potential

0.4 600

"- 770 nm


470) 380

0 450 ____ ________
0 0.2 0.4 0.6 0.8

Figure 2.14. Luminosity or lightness (Y) and chromaticity
(x, y) MacAdam limits for colors viewed in daylight.
[ Adapted from Bi167]