NAT'L INST. OF STAND & TECH R.I.C. ' /gMBi§/:,

AlllDS Sb3nE

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PUBLICATSONS

NisrUnited States Department of Commerce

Technology Administration

National Institute of Standards and Technology

/\I/ST Technical Note 1500-3

Materials Reliability Series

High-Energy, Transmission X-Ray

Diffraction for Monitoring

Turbine-Blade Solidifaction

Dale W. Fitting

William P. Dube

Thomas A. Siewert

QC

100

. 115753

Nai500-

3

1998

NIST Technical Note 1500-3

Materials Reliability Series

High-Energy, Transmission X-Ray

Diffraction for Monitoring

Turbine-Blade Solidifaction

Dale W. Fitting

William P. Dube

Thomas A. Siewert

Materials Reliability Division

Materials Science and Engineering Laboratory

National Institute of Standards and Technology

325 Broadway

Boulder, Colorado 80303-3328

June 1998

'"4TES O*

U.S. DEPARTMENT OF COMMERCE, William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION. Gary R. Bachula, Acting Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Director
National Institute of Standards and Technology Technical Note

Natl. Inst. Stand. Technol., Tech. Note 1500-3, 156 pages (June 1998)

CODEN:NTNOEF

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1998

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
CONTENTS

EXECUTIVE SUMMARY 1

1. INTRODUCTION 2

2. THEORY 4

2.

1

Tutorial on X-Rays and Their Interactions with Matter 4

2.1.1 X-Ray Interactions 4

2. 1.2 Attenuation Coefficients 5

2.2 X-Ray Production 7

2.3 Radiographic Imaging 10

2.4 CoUimation 11

2.5 X-Ray Detectors 12

2.6 X-Ray Diffraction 12

2.7 Implications ofX-Ray Theory for High-Energy Transmission Diffraction 20

3. MODELS OF TRANSMISSION DIFFRACTION 22

3.1 Simple Model, Based on Partial Attenuation Coefficients 22

3.1.1 Advantages and Limitations of the Attenuation Coefficient Model 24

3.1.2 Model Predictions for Metal Specimens 24

3.1.3 Model Predictions for a Mold-Encased Specimen 25

3.1.4 Modeling Various Fractions of Liquid and Solid 25

3.2 Fundamental Physics Model 29

4. APPARATUS 30

4.1 Equipment for High-Energy, Transmission Diffraction 30

4.1.1 X-Ray Source 30

4.1.2 Leakage and Supplemental Shielding 33

4.1.3 Collimators 33

4.1.4 Beamstop 34

4. 1 .5 X-Ray Imager 34

4.1.6 Energy-Sensitive Detector System 37

4.2 Laboratory XRD Apparatus 38

4.3 Gallium Test Cell 40

4.4 Medium-Temperature, Gradient Furnace 41

4.5 Directional-Solidification Furnace 42

4.5.

1

Modifications to the DS Furnace 45

4.5.2 Modeling of Transmission XRD from a Casting in a

Directional-Solidification Furnace 47

4.6 Radiation Safety 47

111
5. DIFFRACTION EXPERIMENTS 51

5.1 Back-Reflection Laue Images 51

5.2 Reflection XRD Experiments 52

5.3 Transmission XRD 52

5.3.1 Single-Crystal Specimens 54

5.3.2 Determining Diffraction Spot Intensity 54

5.3.3 XRD Experiments on a Single Crystal with Amormphous,

Textured, and Crystalline Solids 56

5.3.3.

1

Diffraction Experiments on the Nickel-Alloy Single-Crystal

and Ceramic Mold 56

5.3.3.2 Diffraction Experiments on the Nickel-Alloy Single-Crystal

Surrounded by Fine-Grained Aluminum Plates 58

5.3.3.3 Diffraction Experiments on the Nickel-Alloy Single-Crystal

Surrounded by Coarse-Grained Metal 59

5.4 XRD to Determine the Physical State of a Specimen 60

5.4.1 Liquid-Solid Boundary in Gallium 60

5.4.2 Spatial- Resolution Experiment 61

5.4.3 Diffraction Experiments with the Energy-Sensitive Detector 62

5.4.3.1 Preliminary Experiments to Study Fraction of Solid

Along the X-Ray Beam Path 65

5.5 Medium Temperature (<1000 °C) Furnace Experiments 67

5.5.1 Aluminum Melting Experiments 67

5.5.2 Copper Melting Experiment 69

5.6 Sensing Solidification During Investment Casting 70

5.6.1 XRD Tests in the Directional Solidification Furnace 76

5.6.2 Experiments with the Germanium Detector 78

5.6.3 Producing Single-Crystal Castings 78

5.6.4 XRD During Investment Casting 81

5.6.3.1 Probing the Dendritic Region of Solidification 84

5.6.3.2 X-Ray Topography of Dendrites During Solidification 87

6. CONCLUSIONS 90

7. PATENT 90

8. REFERENCES 91

9. BIBLIOGRAPHY 93

10. APPENDICES 94

10.1 Tables of X-Ray Attenuation Coefficients as a Function of Energy 94

10.2 Physical Properties of Metals Used in the XRD Experiments 119

10.3 Composition of N5 Nickel Alloy 119

10.4 Anomalous Dispersion Corrections for Nickel 120

10.5 Model of Transmission XRD from a Sample Surrounded by Mold Material .... 122

10.6 Patent 138

IV
FOREWORD

The Materials Reliability Series of NIST Technical Notes are reports covering significant

research accomplishments of the Materials Reliability Division. The Division develops

measurement technologies that enable the producers and users of materials to improve the quality

and reliability of their products. Measurement technologies are developed for process control to improve the quality and consistency of materials, for nondestructive evaluation to assure quality

of finished materials and products, and for materials evaluation to assure reliable performance.

Within these broad areas of measurement technology, the Division has focused its resources on

three research themes:

• Intelligent Processing of Materials—To develop on-line sensors for measuring the

materials' characteristics and/or processing conditions needed for real-time process

control.

• Ultrasonic Characterization of Materials—To develop ultrasonic measurements for

characterizing internal geometries of materials, such as defects, microstructures, and

lattice distortions.

• Micrometer-Scale Measurements for Materials Evaluation—To develop measurement

techniques for evaluating the mechanical, thermal, and magnetic behavior of thin films

and coatings at the appropriate size scale.

This report is the third in the Materials Reliability Series. It covers research on high-energy

transmission X-ray diffraction for monitoring turbine-blade solidification. Previous reports in

this series are:

Technical Note 1500-1 Tensile Testing of Thin Films: Techniques and Results,

byD.T. Read, 1997

Technical Note 1500-2 Procedures for the Electron-Beam Moire Technique,

by E.R. Drexler, 1998

HIGH-ENERGY, TRANSMISSION X-RAY DIFFRACTION FOR

MONITORING TURBINE-BLADE SOLIDIFICATION

Dale W. Fitting, William P. Dube, and Thomas A. Siewert

Materials Reliability Division

Materials Science and Engineering Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303

We developed a nondestructive x-ray technique to monitor the solidification of singlecrystal turbine blade castings. X-ray energies in the 150 keV to 300 keV range have

sufficient energy for transmission x-ray diffraction to be performed on a 12 mm thick

nickel-alloy specimen. We obtained diffraction images even though the x-ray path (over

1 m) through a directional solidification furnace included glass fiarnace ports, molybdenum

heater windings, an aluminum oxide heater-coil support, and mold material. The method

was capable of sensing changes in the physical state of the casting (liquid, dendrite, solid)

and measuring the solid fraction in the mushy zone.

Keywords: diffraction, directional solidification, investment casting, single-crystal, x-ray

EXECUTIVE SUMMARY

We developed a technique based on transmission x-ray diffraction (XRD) to study the

solidification of a single-crystal turbine blade casting within its mold. High-energy x-rays

penetrate through material surrounding the casting and produce a distinctive diffraction pattern

which clearly indicates whether the sampled region is liquid or solid. A real-time transmission

Laue x-ray image of the casting shows an ordered pattern of x-ray scattering (diffraction spots)

from the solid and a diffuse ring of scattering from the liquid. The dramatically different spatial

pattern provides a high-contrast, unequivocal spatial discrimination of the physical state of the

alloy.

Proof-of-concept experiments were performed on aluminum and copper melted in a gradient

fijrnace. Laue images and transmission energy spectra proved to be highly sensitive means for

identifying the presence of liquid or solid material in the casting.

We have successfully performed real-time transmission XRD on a casting of N5 nickel-alloy in an industrial furnace for casting turbine blades. The high energies (up to 320 keV), permitted

transmission XRD to be performed on a specimen 12 mm thick. XRD images were obtained even though the x-ray path through the fiarnace included 20 mm of borosilicate glass (furnace ports),

3.2 mm of molybdenum (furnace hot-zone windings), 9 mm of aluminum oxide (hot-zone coil

support), and 12.8 mm of mold material (refractory oxides). The distance from x-ray source to
imager was 1 180 mm. Motion-control stages permitted scanning of both the x-ray source and the

detector to follow the casting during withdrawal and to probe the mushy zone. The x-ray

diffraction spot intensity was high when the probing x-ray beam was directed into the solid, and

decreased when the x-ray beam was scanned vertically into the molten alloy. Plots of diffraction

spot intensity versus vertical position (increasing temperature) in the casting correlate well with

Lever-law model predictions of fraction solid versus temperature.

Accomplishments

• We developed high-energy, transmission x-ray diffraction as a noninvasive means for locating

and characterizing the liquid-dendrite-soUd region in a single-crystal investment casting during

directional solidification.

• We demonstrated the x-ray diffraction sensing technology on a mold-encased nickel alloy

(N5) specimen in a turbine-blade casting furnace.

• We developed an analytical model for high-energy transmission diffraction and used it to

optimize the diffraction system for specific mold/sample configurations.

• We received a patent on the transmission diffraction technique for monitoring solidification of

a casting within its mold.

1. INTRODUCTION

TheNIST Consortium on Casting of Aerospace Alloys, an industry/government/university

team, was organized in 1994 to improve quality and reduce cost of aerospace castings through

advances in materials science. The Consortium identified several areas where developments in

technology would substantially improve the investment casting process. In particular, no sensor had been capable of locating the liquid-dendrite-solid region in the harsh environment of a turbineblade casting furnace (high vacuum, high temperatures, and strong radio frequency fields).

A variety of sensing technologies (x-ray imaging, ultrasonics) have been used to study metal

castings [1-5]. Yet, few techniques are suitable for process sensing when the metal is encased in a

thick ceramic mold with irregular interior and exterior geometry. We have developed a

transmission x-ray diffraction sensor capable of monitoring the position, shape, and extent of the

liquid-dendrite-solid region (mushy zone) in single-crystal turbine-blade castings.

The technique is capable of sensing the physical state of the casting even though the casting is enclosed in a thick ceramic mold and contained within a vacuum fiirnace. The high contrast

(many times greater than that for a conventional x-ray imaging technique) of the XRD sensor is achieved because of the strikingly different x-ray diffraction patterns from a solid versus a liquid.
An x-ray beam directed into a crystalline material will diffract sharply from the lattice planes. The

spatial distribution of the diffracted x-rays depends on the spacing of the crystalline planes and the

orientation of the x-ray beam with respect to these planes. However, the emergence of any

geometric pattern in the scattering indicates the presence of an ordered structure. X-ray

scattering from a liquid is relatively amorphous, with only a single broad peak in its radial

distribution. Thus, the presence or absence of a sharp geometric pattern of diffracted x-rays

forms the basis for a sensing method for demarcating the liquid-solid boundary in a single-crystal

casting. In addition to sensing the position of the solidification front, the XRD method has been

used to determine the extent and shape of the mushy zone in a casting of nickel superalloy.

Analytical x-ray diffraction is conducted in the reflection geometry using x-ray energies in the

5 to 17 keV range. This technique returns crystal structure information from only the surface and

several micrometers beneath it. Since the penetration depth of low-energy x-rays is shallow,

traditional x-ray diffraction is thus unable to probe the interior of thicker structures. Synchrotron

radiation, producing x-ray energies of 100 keV and higher, permits the study of specimens up to a

few-millimeters thick [6,7]. In this.paper, we show that melting and solidification of a centimeterthick metallic specimen within a mold can be monitored by using x-rays of higher energies, 150 to 300 keV, and a transmission configuration.

Using x-ray diffraction to study metal solidification and phase changes is not new [8-14].

However, most of this prior research used very thin (a few millimimeters at most) specimens,

furnaces with low-attenuation x-ray windows (beryllium, graphite, or polyimide), and low (less

than 50 keV) x-ray energies. Work by Green [15] extended x-ray diffraction investigations to energies exceeding 150 keV. His flash x-ray diffraction system also provided the facility for

studying structural changes during dynamic events, such as crystal growth. Others, including

Kopinek, et al. [16] and Bechtoldt, et al. [17] have employed high-energy XRD for studies of

stress and texture in thick (up to 12.7 mm) steel specimens.

Probing the interior of a casting requires a transmission configuration. X-ray energies of

over 150 keV are needed to penetrate the refractory oxide mold (5 to 10 mm wall thickness) and

casting specimen (1 to 10 mm thick). These x-rays have energy sufficient to penetrate the furnace

components, mold, and alloy specimen, while retaining a moderate cross section for diffraction.

The work reported herein shows that melting and solidification of a thick metal specimen can be

detected nondestructively from the spatial distribution or energy spectrum of diffracted x-rays.

Solidification sensing is carried out in the following manner. An x-ray beam of small

diameter is directed into the material being cast. Detection of only spots indicates a fully solid

structure, detection of only a diffuse ring indicates a fully liquid region, and detection of a combination of spots and diffuse ring indicates a mixture of liquid and solid. The relative

intensities of the spots and ring are proportional to the fraction of solid and fraction of liquid

(respectively) present at any location. Scanning the x-ray source and detector to move the region

probed by the x-ray beam may be used to locate the mushy zone in an alloy casting.
2. THEORY

An understanding of x-ray physics is required in sections of this report, Therefore, we present

a brief tutorial. Additional information may be found in references 18 through 20.

2.1 Tutorial on X-Rays and Their Interactions with Matter

X-rays are electromagnetic waves with an energy in the 1 keV to 50 MeV range. The

wavelength (A), frequency (/), and speed (c) are related through the expression

c = ^f. (1)

The energy carried by an x-ray is E = h c ^'

(2)

where

h is Planck's constant (6.626076 x 10'^'* J-s), and

c is the speed of light (2.997925 x 10* m/s, in vacuum).

With i in nm and E in keV, the expression becomes

j:, 1.239842 ^ - -, (3)

For wavelengths in the few nanometer range (atomic dimensions), the corresponding energy of an

x-ray photon is a few kiloelectronvolts (1 kev = 1.602177 x 10"^^ J).

2.1.1 X-Ray Interactions

Below energies of 1.02 MeV, x-ray photons interact primarily with the electrons of atoms, by

photoelectric absorption, Compton scattering, or elastic scattering. In a photoelectric interaction

the incident x-ray energy is totally transferred to an electron, usually an inner-shell electron. If the

energy imparted during the interaction is larger than the binding energy of that electron, the

electron is ejected from the atom. The kinetic energy of the electron is equal to the incident x-ray

energy minus the binding energy of the electron. The resulting electronic structure of the atom is unstable. Stability is restored when the vacancy is filled by a more loosely bound (outer shell)

electron. During this transition, a photon, with energy equal to the difference in binding energies

of the inner and outer shells is released from the atom. This process is termed fluorescence

radiation. During some outer to inner shell transitions, the energy is imparted to an electron,

4
rather than being released as a photon. The ejected electron is called an Auger electron. The

energy of the emitted radiation (photon or electron) is characteristic of the atom, and may be used

identify the element.

X-ray interactions with loosely bound, outer shell electrons occur by Compton scattering.

The electron is ejected and the incident photon (with decreased energy and momentum, and

increased wavelength) is scattered incoherently. The phase of the scattered x-ray is not related to

that of the incident x-ray; it is random. Incoherent Compton scattering is usually a nuisance in x- ray imaging or diffraction studies—it contributes to the background and carries little useful

information.

An x-ray photon may also be elastically scattered from an electron in an atom. The electric

field of the incident x-ray causes the electron to oscillate. The moving charge reradiates the

electromagnetic wave with no energy loss. Because the phase of the incident and reradiated

electromagnetic field are directly related the process is termed coherent scattering. It is the

coherence of this process which generates x-ray diffraction.

2.1.2 Attenuation Coefficients

Interactions of a narrow beam of monoenergetic x-rays with matter may be characterized with

a total mass attenuation coefficient (|i/p). The intensity of x-rays transmitted (at perpendicular

incidence) through a slab of material is given by

u I = I,e ^ , (4)

where

Iq is the incident x-ray intensity,

/ is the transmitted x-ray intensity,

ji/p is the mass attenuation coefficient (a function of x-ray energy),

p is the density of the material, and

jc is the thickness of the material.

Figure 1 illustrates the behavior of transmitted intensity by plotting fractional transmission ///q as a function of the material thickness. Raising x-ray energy increases transmission, because the

attenuation coefficient decreases with energy.

A linear attenuation coefficient (//), defined as the product of the mass attenuation coefficient

and the density, is useful for comparing the relative transmission through different materials of the same thickness. The reciprocal of the linear attenuation coefficient (that thickness of material

which reduces the intensity to 1/e) is often used as a measure of the effective penetration depth

for x-rays. Plots of 1/// for several materials are shown in Figure 2.
12 3 4 5

Thickness (cm)

Figure 1 . Fractional transmitted intensity decreases exponentially with thickness (shown here for

nickel); transmission depends on photon energy.

100 200 300

X-Ray Energy (keV)

400 500

Figure 2. Reciprocal, \/ju, of the linear attenuation coefficient, ju, as a function of x-ray energy.

The physical meaning of \//j is the effective penetration depth.
The total mass attenuation coefficient may be expressed in terms of a sum of partial mass

attenuation coefficients, which reveal the contributions by the photoelectric {PE), Compton

(Comp), and coherent (coh) processes.

(^) - (i^) -(i) *(^)

r total P PE P Comp P coh (5)

Partial and total mass attenuation coefficients for all elements and a variety of mixtures and

compounds have been tabulated [21]. Software is also available for calculating attenuation

coefficients [22]. Plots of attenuation coefficients for several materials as a function of energy are shown in Figures 3 through 6. The attenuation coefficients are significantly larger for nickel and

tungsten having higher atomic number and density, than for aluminum or the mold material (a

mixture of refractory oxides—alumina, zirconia, and silica). The abrupt change in attenuation

coefficient at particular energies (refer to the plot for tungsten) is termed an absorption edge. It represents the increased probability of interaction of an x-ray with a material when the x-ray

energy is sufficient to eject a bound electron by the photoelectric effect. Absorption edges for

aluminum, nickel and the mold material occur at energies lower than 20 keV. Partial and total mass attenuation coefficients for many of the materials used in our studies of x-ray diffraction may

be found in the appendices.

The dominant interactions of x-rays with matter are the photoelectric process at low energies

and Compton scattering at higher energies. Although coherent scattering is not a large

contributor to the total attenuation, this interaction does occur at high energies.

2.2 X-Ray Production

X-rays are produced when a moving charged particle interacts with a target material. In a conventional x-ray tube, electrons ejected from a heated filament (cathode) are accelerated by a high voltage toward a metal anode. If an incident electron ejects an electron from an atom in the

anode, the vacancy in the electron shell is filled by an electron from an outer shell. During the

transition, an x-ray of specific energy is produced. The energy of the x-ray is characterisitic of the

shell transition within the anode material. When the innermost shell electrons are ejected, Kcharacteristic x-rays are produced. KKj, Ka2, and KPj x-rays of discrete energies are produced

when electrons from the L3, LI, and M3 shells fill a K-shell vacancy. The intensity (4/,ar) of

characteristic x-rays is linearly related to the current (/) passing through the tube and the

difference between the tube potential (V) and the threshold value iV,i,resh) of the potential for

producing a specific characterisitic x-ray line.

^char = C,nV-V,,^^J\ (6)

where Cj is a constant, and n is approximately 1.5.
E

o

o

0)oO

c

o

COD

C

COC

1E3

1E2

1E1

1E0

1E-1

1E-2

1E-3

1E-4

^

1

1 1 1 1 1 1 1 1 ^^

-»- Coherent -"^^ Compton -•- PE ^&^ TOTAL

h=H

^—%-

\^ ig,^ —

W+ti)TMWatt*nwBa siSisas Ef^es^ariSri! n.[—^^"^^ ^^

^e%!^ ^^^

»Nessi -^^ii«iaMtmrtTFi II ^••^1

^^^IIB \i ^^»*iS^^^=

100 200 300

X-Ray Energy (keV)

400 500

Figure 3. Partial and total linear attenuation coefficients for aluminum (Al) as a function of x-ray

energy.

1E3 ^nt^rn^ E

o

T— 1E2

(/) *-> i- 1E1

o^

o 1E0

O

c

o 1E-1

CD3

1E-2 *^<L_

(0 1E-3

c

1E-4

^^=^^

^

—"— ^^onereru ^«^ v^ompion —•— re —<*— iuiml

^^

\ ^M—

1

V- —^

-^ 1

1 ^v—

^^^^^

- ^^5=^ h==z— .

. — .^^Bi

, T T , 'V T * ^^^iMb "WfTg^ ^^g^^ ^^^^SSB

Z!!EsaBg *"«««.r*^ ^^^"••m^ ^

k^"MBW ffififtM )Amm

—^—==]

100 200 300

X-Ray Energy (keV)

400 500

Figure 4. Partial and total linear attenuation coefficients for nickel (Ni) as a fiinction of x-ray

energy.
E

o

w

c

o

<DOO

c

o

c5c

3=: <

CO

(Dc

1E3

1E2

1E1

1E0

1E-1

1E-2

1E-3

1E-4

^

^v^I ^ —«

%

^

ta ^^^m-w^

^ba&,ft=^ ^h^

**<&< ^

^ifet--

w^ '^'^fm m^ ^A-A-A-^ft^ -^^^^inS««W«*^ "4»5Sk5'KXk^^S^3 c^2^J^;c^ NMW^

Tri^

D^«!M«mmi ^''^''^'MSt

- r-H- Coherent -^^ Compton -•- PE -^^^ Total

|

\ \\ \\ \1

\ 1 100 200 300

X-Ray Energy (keV)

400 500

Figure 5. Partial and total linear attenuation coefficients for tungsten (W) as a function of x-ray

energy.

E

o

c

o

o

(UoO

c

o

(0C

CD

CD

CDC

1E3

1E2

1E1

1E0

1E-1

1E-2

1E-3

1E-4

M —Pi

Coherent v Cnmntnn —•— PF a. TDTAI M

f

-^v- -^—

fw;r- w ps^^^^ a^SwAmfe^p«=H=#=iS^^3$^^ ^^^SKS^SJfH ^^^,J - Sm •^ ^

==»«(

**=!*;^kjOD ^***ii »^ — »«teji^^ I!!!^ ^^n^mn^mss^<»«w^

'*M^B|-HM-

=

100 200 300

X-Ray Energy (keV)

400 500

Figure 6. Partial and total linear attenuation coefficients for the mold material (mixture of

alumina, zirconia, and silica) used to make single-crystal turbine blade castings.
Electrons accelerated in the x-ray tube can also interact with the nuclei of anode atoms. The

attractive force between the positively charged nucleus and a negatively charged electron can slow the electron. The decelerating charge emits electromagnetic radiation in the form of

bremstrahlung x-rays. Because the interaction can be weak or strong, depending on the proximity

of the electron to the nucleus, the x-ray energy can range continuously from a small value to the

total kinetic energy of the electron. The energy of the electrons, in keV, is numerically equal to the tube potential, in kV (100 keV maximum energy with a 100 kV tube potential). Kulenkampf

[23] developed an empirical relationship for the intensity of the bremstrahlung radiation produced

at a particular wavelength. We have rewritten the relationship here, in terms of energy (£).

I{E) = CZ E'iE^^^-E) ^B Z' E' , (7)

where

C and B are constants, with C »B,

Z is the atomic number of the anode, and

E^^ is the highest energy in the x-ray spectrum.

Integrating intensity over all energies in the bremstrahlung spectrum gives

h

= C,iZV\ (8)

where Q is a constant.

The spectrum of energies from an x-ray tube is a composite of these interactions, yielding a continuous spectrum produced by bremstrahlung interactions, overlaid with characteristic x-ray

peaks. Increasing the tube potential (F) dramatically increases the intensity of both characteristic

and bremstrahlung radiation. X-ray intensity increases linearly with tube current (/). Figure 7 is an x-ray spectrum, measured experimentally, from a tungsten-target tube, operated at a tube

potential of 75 kV. Significant features are the smooth bremstrahlung spectrum with a maximum

energy of 75 keV, the intense characteristic x-ray peaks (at 58.0, 59.3, 67.2 keV) from the

tungsten anode, and a maximum intensity in the bremstrahlung spectrum at approximately onethird of the maximum energy.

2.3 Radiographic Imaging

The interior structure of optically opaque materials may be examined by radiographic imaging.

The specimen is illuminated by a large-area x-ray field. X-rays transmitted by the specimen are recorded on a two-dimensional x-ray sensitive medium. The image receptor might be a sheet of

film or an electronic device which responds to x-rays. Transmission by the specimen depends on

the attenuation coefficient, density, and thickness. Since the attenuation coefficient is a function

of energy, the choice of x-ray tube voltage will affect the contrast of the radiographic image.

10
10000

8000

lU 6000

o

4000

c

2000

30 40 50 60

X-Ray Energy (keV)

70

Figure 7. Spectrum of x-rays from a tube with a tungsten anode. Tube potential

current = 0.2 mA, source-to-detector distance = 960 mm.

80

75 kV, tube

2.4 Collimation

Certain x-ray procedures (such as diffraction) require that the x-ray beam is restricted to a very narrow beam. Collimators perform this task. X-ray collimators generally do not make the

rays parallel (as do optical collimators) but simply restrict the emerging rays to a narrow range of

angles [24]. Apertures or slits in a very attenuating material (lead, tungsten) are commonly used.

Figure 8 shows the geometry of a set of coUimating apertures. The maximum divergence angle is given by

'»"(P/2) = ^, (9)

where the angles are defined in Fig. 8. Since the angle /?is small,

u

(10)

where /? is in radians.

11
^---. ^___^^_i^.---^-_ L ^^ ^ ^ ^ "\

h

W

C

Figure 8. CoUimating apertures may be used to limit the angular spread of an x-ray beam.

Penumbra (unsharpness at the edges) in the collimated beam is minimized by choosing the source size (focal spot) and collimator aperture to be equal. Small apertures, spaced far apart will

restrict the angular divergence of the beam. However, reducing the collimating apertures

decreases the available x-ray intensity by limiting the area of the beam.

2.5 X-Ray Detectors

X-ray imaging or measurements require a device for measuring the intensity of an x-ray beam.

Silver bromide grains in film undergo a change in energy state when exposed to x-rays. Chemical

processing causes silver in these affected film grains to precipitate, producing a dark spot on the

film. Film is able to record the two-dimensional distribution of x-ray intensities, and so is useful

for radiographic imaging. Two other types of detectors were used in our research—a real time

imaging device and an energy-sensitive germanium detector. Both are discussed in detail later in

this report.

2.6 X-Ray Diffraction (XRD)

Constructive interference of coherently scattered x-rays produces diffraction. Since coherent

scattering is an interaction of an electromagnetic wave with atomic electrons, let us begin by

examining the scattering from a single electron. Thomson described the scattering of an

unpolarized electromagnetic wave from a single electron with the equation [18]

p

[l+cos2(20)]

R^ m^ c'

1

471 Eq

2

-) , (11)

12
where

Ip is the scattered intensity, e is the charge of an electron,

R is the distance from the electron where the intensity is measured,

m is the mass of an electron, c is the speed of light in a vacuum,

2^ is the angle between the incident and scattered directions, and

€q the dielectric constant of free space.

Evaluating the constant term gives

(^—) = 7.88 X 10-30 ^^2-|

4 (12) m^ c^ 4tu e

However, in 1 mg of material there are over 10^° electrons, and ati? = 10"' m,

'j- -~ 10-' . (13)

Although this ratio seems small, it is easily detected.

Next, consider scattering from the cloud of electrons surrounding an atom. Figure 9 shows a

plane electromagnetic wave incident upon an atom. Suppose coherent scattering from two of the

electrons occurs. Because the path lengths travelled by the electromagnetic waves differ, the

waves scattered to the point of observation will differ in phase. Interference of the scattered waves will depend upon the location of the electrons (spatial probability density distribution), on

the scattering angle {20), and on the wavelength of the incident wave. An atomic scattering

factor (/") which describes this interference, may be calculated for a particular atom or ion using a quantum mechanical approach. The atomic scattering factor (sometimes called the form factor) is

/ = ^. (14)

where

£„,„„ is the electric field scattered from an atom, and

E^ is the field scattered from a single electron (that is Thomson scattering).

In general,/will be a complex number [25], where

Re(f)-f,-f'-f^T^ f-A-frel-^^ (15)

13
Figure 9. Diagram demonstrating coherent scattering of an electromagnetic wave, incident from

the left, on two electrons in an atom.

and

Im(f) =f" =/, = E |ip^ u A

Ihcr, (16)

where

E is the photon energy,

/o is the coherent scattering factor,

ffjj is the nuclear Thomson factor,

f^^i is the relativistic correction factor, u is the atomic mass unit (1/12 the mass of an atom of ^^C),

A is the relative atomic mass of the material, and

r^ is the radius of an electron.

The terms/ ' and/ " are called the anomalous dispersion corrections. They are especially

significant near the absorption edges of the scattering atom. / and/ are functions of energy and

atomic number, and/ is a function of the momentum transfer (4tu sm(d)/A) and energy, f^j and

^ei are small, negative numbers. Equation (16) also shows the imaginary part of the dispersion

correction is related to the photoelectric attenuation coefficient. The real and imaginary

components of/have been calculated, and are tabulated [25]. Plots off/E) and/fEj for nickel are shown in Figures 10 and 11, respectively.

In some of our models we use an empirical fit [26]

/o = E^, exp[-Z). i^f] + c

; = 1 A

(17)

14
29 1

I

27

r26

^25

•i24

(D I 23

o

in

22

21

I i

iii

10 100

X-Ray Energy (keV)

1000

Figure 10. Plot of/;, for nickel, as a function of energy, fj approximates the real part of/in the

forward direction.

D

^~^f\ - E^

o V ^ I

I- T O 'I \

i V

CD O

U_ ' \ T

c \ \

(0o

CO 1 -

iL V \f

1 w \

s

S

^r ^k

-

^v ^[s^sa ^Lww»«www9mw- 10 100

X-Ray Energy (keV)

1000

Figure 11. Plot of f2, for nickel, as a function of energy. / can be related to the partial

attenuation coefficient for photelectric interactions.

15
to the coherent scattering factor. The constants a; , bj, and c depend upon the atom. Plots of

atomic scattering factor for several different elements are shown in Figure 12, as a function of

{sm6/A). In the forward direction (^=0), scattering from all electrons is in phase, so the

scattering factor is equal to the number of electrons (Z). The energy and angular dependence of

the scattering factor is demonstrated in Figure 13, which plots the atomic scattering factor for

nickel. For high energies, the scattering becomes increasingly forward-directed.

The next level of complexity is to consider x-ray diffraction from the unit cell of a crystal,

where the structure (position of atoms) is fixed. A structure factor (F) is defined as [18]

^ = E A exp[/^ {S-S,)-rJ = E /„ exp[/27T (hx„ ^ ky„ -^ lz„)] ,

1 A 1 (18)

where

/„ is the atomic scattering factor of the mh of the A'' atoms in the unit cell, Sg and S are vectors in the directions of the incident and the scattered x-rays, respectively,

r„ is a vector from the origin of the unit cell to each of the atoms,

hkl are the integer Miller indices of a set of lattice planes in the crystal, and

x„, y„, z„ are the relative positions of atoms in the unit cell.

0.2 0.4 0.6

sin( )/

0.8 1.2

Figure 12. Atomic scattering factor for several materials plotted as a flinction of (sin ^/i).

16
o

o

(0 u_c

0)

00o

(/) o

E

o

<

30

25

20

15

10

^^ ^^

40keV / %\ ^

//>

Yv\\

100 k

^/1// \

^

\l50keV

^

200 ke'\y V^JOO keV^

10 -5 5

Scattering Angle (degrees)

10

Figure 13. Atomic scattering factor at particular x-ray energies, for nickel, plotted as a function

of scattering angle {2d).

As an example, consider a nickel crystal, which has a face-centered cubic structure. The

relative atomic positions in the unit cell are 000, '^'^O, '/20'/2, ^ViVi. We use the second form of

the structure factor in eq (18) to write

P - f

r Qi2n(h0^k0^l0) ^

^iluQill+kl+lO) ^

^i2n{h2+kO+l/2) ^ iln (/)0+/t/2+//2)

] . (19)

If /?, k, and / are mixed (even and odd), then F = 0. If the indices {hkl) are unmixed (all even or all odd), then F = 4 f^j , and FF* = 16 f^jl

The intensity (/) scattered by a unit cell is then

e^ [l+cos2(20)] / = L-F-F*-

R^ m^ c^

1 2

471 e^ (20)

Diffracted intensity will increase with the number of unit cells illuminated by the x-ray beam. For

a small single crystal, illuminated by an unpolarized x-ray beam, the scattered intensity is [18]

17
'p - ^ -^r-7 :r-^ (——) ^ ^ 11 1 ' (2i)

i?2 trj^ c^ 4tu e '=» sm\:^{S-S,)'a^)

where

a, are the vectors that define the crystal axes, and

Nj is the number of unit cells in the crystal, in the direction a,

.

Note that the last terms are of the form [sin^f7\^ysin^(3^j], and that

sin^CA^;^) ^ (M. ^ N'

sirriy) as y ^ niz

y

(22)

Figure 14 shows [sin^(7\^ysin^(3^j] plotted versus j', for two values ofA^. Note that the peak is highly localized, that the peak height goes up as 7V^ , and that the value of the function is approximately zero except at integer values of tt. This illustrates the behavior of the diffraction

process, which yields high diffracted intensities in certain directions and negligible intensities in all other directions. The product, A^/ A^/ N^^ will be very large even for a small crystal.

100 1

80

60

40

20

10000

8000

6000

4000

2000

A A

1 ;kt^ in 1 ' M

\

I \ M^

\^ - — ^/ \ ^^^ — - - ^

.a/ ^/^|

:nm \m

i— L^ A

2 3 4

y

Figure 14. [s\Y^(Ny)/s\T^(y)'\ plotted versus y, forN= 10 and A'^= 100. There are maxima aty=n7r.

18
Diffraction occurs when

jiS-So) -a. = nn . (23)

These conditions, usually written

{S -Sq) • ofj ^ hn

(S-Yq) a'^^ k-K (24)

(S-Sq) • a^ = It: ,

are known as the Laue equations. The integers hkl are the Miller indices of a particular crystalline

lattice plane.

Often, a simpler form of the diffraction conditions is used. The Bragg equation

tiX = 1.24 - = 2af sin(0) , (25) E

wheren is an integer,

A is the wavelength of the x-rays (nm)

E is the energy of the x-rays (keV),

d is the lattice spacing (nm), and

2^ is the angle between the incident and diffi-acted x-ray,

expresses these conditions. Figure 15 illustrates that the Bragg equation describes the situation

when the difference (AOB) in path length for x-rays "reflected" from adjacent lattice planes is an

integer number of wavelengths (that is constructive interference occurs).

The diffi^action interaction is thus a spatial (0) and energy (£) filter. X-rays of higher energy

coherently interfere at smaller angles. An x-ray imager placed in the diffraction field records the

spatial location of diffracted x-rays. An energy-sensitive detector placed at the same location as the imager would record energy peaks associated with each of the diffraction spots.

Raising the temperature of the specimen decreases the diffracted intensity because the atoms

move out of the mean position where diffraction occurs. Multiplying eq (21) by e'^^ (the Debye

temperature factor) gives the correct intensity. The factor 2M = 167iius)^ (sirid/A^), where {us) is the component of the mean displacement in the direction normal to the diffracting planes. This

correction for temperature is applicable when all atoms in the small, diffracting crystal are the same.

19
Incident

Plane

Wave \ ^ Wave

Diffracted

Figure 15. Diffraction occurs when the path length difference (AOB) between reflections is an

integral number of wavelengths.

2.7 Implications of X-Ray Theory for High-Energy Transmission Diffraction

Probing the interior of a casting requires a transmission configuration. X-rays energies of

over 100 keV are needed to penetrate the refractory oxide mold (5 to 10 mm wall thickness) and

casting specimen (1 to 20 mm thick). Below, we explore the physics of using high-energy x-rays

to produce transmission x-ray diffraction.

Consider the situation shown in Figure 16, of a beam of x-rays incident on a crystalline

specimen contained within a casting mold. The primary x-ray beam is attenuated as it passes

through the mold wall and a portion of the specimen, to a location where coherent scattering occurs. The scattered x-ray is attenuated along its exit path through the remaining specimen and

exit mold wall. Attenuation losses (refer to Figs. 3 through 6) along entrance and exit paths are minimized by raising the energy substantially above that (5 to 20 keV) used in conventional x-ray

diffraction systems to 150 to 300 keV.

The intensity of elastic scattering from a crystalline solid, given in eq (21), is the product of

the squared structure factor (F) of the crystal, the Thomson scattering amplitude from an isolated

electron, and the squares of the number of unit cells along the three crystalline axes. Fis a function of the types of atoms in the crystal (through the atomic scattering factor, y), the

configuration of the unit cell of the crystal, and the particular lattice planes which are involved in the scattering. For a face-centered cubic (fee) crystal, such as nickel, the structure factor is equal

to ^if the Miller indices ihkl) are unmixed (all odd or all even), but is zero if the indices are mixed. The intensity of the scattering is the square of the amplitude. The structure factor is thus

squared, to give 16p for an fee material with lattice planes defined by unmixed Miller indices.

The dependence of the atomic scattering factor for nickel was plotted in Figure 13, as a function of the scattering angle for several x-ray energies. At low x-ray energies, the atomic

20
scattering factor is quite large, even for large scattering angles. However, with high x-ray

energies, /is significant only for small scattering angles, that is, for a transmission geometry. For

example, the scattering factor for nickel is 16.5 for 150 keV x-rays scattered at 3.5° from the

direction of the incident x-ray beam (typical of our experimental geometry). The structure factor

squared for this example is 16 x (16.5)^ , or 4356.

For a nickel crystal 0.001 mm x 0.001 mm x 0.001 mm, A^/ = TV, = TV^ = 2.8 x 10^ so the

product A^;' X N,' x N,' - 5 x lO'*'.

The atomic scattering factor in the forward direction, the enormous number of unit cells along

the path of the primary beam (all with the same crystalline structure and orientation), in addition

to the substantial intensity of high-energy x-rays which penetrate through a mold and specimen, all account for the efficiency of high-energy transmission diffraction.

Diffracted

X-Rays

Incident

X-Ray Beam

Figure 16. Geometry of transmission diffraction from a crystalline specimen surrounded by a

casting mold.

21
3. MODELING TRANSMISSION DIFFRACTION

We studied the effects of properties and thicknesses of casting alloy and mold theoretically, to

guide our development of transmission x-ray diffraction (XRD). A simple radiation transport

model was developed to study x-ray diffraction from a specimen encased within a mold. The

model has proven useful for determining the range of x-ray energies optimal for transmission x- ray diffraction. The model predicts the fraction of incident x-rays emerging as coherent radiation

(which can produce diffraction), in the direction of a detector, from a metal specimen encased in a mold.

For in-situ casting measurements, x-rays from the source encounter a mold wall, then the

specimen, another mold wall, and finally an x-ray detector. In addition, the beam may pass

through some distance in air and perhaps furnace walls. The severity of the attenuation along this

path depends on the x-ray attenuation coefficients, and densities, and thicknesses of the materials

encountered. The attenuation coefficients depend on the incident x-ray energy. The model

accounts for attenuation along the path (furnace and mold walls) of the entrance beam,

attenuation in the specimen to the location of scattering, the efficiency of production of coherent

scattering in the specimen, and the attenuation along the exit path (remaining specimen, mold

wall, and fiirnace wall) of the scattered beam. The spatial distribution of diffracted radiation,

which is approximated in this simple model by assuming that a fixed portion is forward-directed,

determines the fraction of the scattering fluence which is potentially detectable by the x-ray

detector. A fixed value of 0.007 for the forward directed fraction, based on our experimental

geometry, was used in the model calculations reported here.

3.1 Simple Model, Based on Partial Attenuation Coefficients

Figure 17 shows the components necessary to perform transmission XRD. X-rays from the source are collimated into a narrow beam by a set of apertures. This narrow beam encounters an

entrance mold wall, then the specimen, the exit mold wall, and finally an x-ray detector. X-rays

entering the mold are attenuated. Attenuation also occurs in the specimen to the depth where

coherent scattering occurs. X-rays diffracted from this volume element in the specimen are attenuated as they pass through the remaining specimen and the exit mold wall. The severity of

the attenuation depends on the attenuation coefficients in the mold and specimen, the thicknesses,

and densities of the materials, and the energy of the x-rays. Diffraction by an element of the

specimen also depends on the specimen material and the x-ray energy. The processes of

attenuation and diffraction are modeled to give insight into transmission XRD.

Let Iq(E) be the x-ray intensity (at energy E) incident upon the detector with no specimen or mold present. The x-ray intensity which is transmitted through the entrance mold wall is

/.(£)=/„(£).'"-'"""-"''', (26)

22
where

//„, (E) is the total mass attenuation coefficient of the mold wall,

p^ is the density of the mold wall, and

Wj is the thickness of the entrance mold wall.

Let I2 (E) be the intensity of coherent scatter which emerges from the specimen. I2 depends

upon: (1) the attenuation in the specimen from the entrance surface to the location where

coherent scattering occurs, (2) the efficiency of generation of coherent scatter, and (3) the

attenuation of the coherent radiation as it passes through the remainder of the specimen.

Summing the effects of the loss and generation mechanisms for all elements through the thickness

of the specimen gives

N

I,(E) = I,{E) E e

-\^s,(^Ps"dx [Ki\-e -\^sr(^Ps^-)]e -i^s,Ps(L-"'^)

(27)

«=i

where

//^, (E) is the total mass attenuation coefficient in the specimen,

p^ is the density of the specimen,

A'' is a large number which partitions the specimen length Z into length segments dx,

K is the fraction of coherently scattered photons which potentially could contribute to a

transmission diffraction pattern, and

ju^i^ (E) is the partial mass attenuation coefficient for coherent scattering in the specimen.

The negative exponential in the second term of the summation represents the loss from the narrow beam due to production of coherent radiation. Since the scattering is isotropic, a fraction

Mold

Walls

LLLLU

-LLLL

.LLLL _LLLL

-LLLL

-LLLL

X-Ray

Source .LLLL

.LLLL

.LLLL

.LLLL

.LLLL

.LLLL

^ W1 ^

Casting

Specimen

LLLLU

LLLLI

LLLLI LLLLI

LLLLI

LLLLI

LLLLI

LLLLI

LLLLI LLLLI

LLLLI

LLLLI LLLLI

^W2NFigure 17. Geometry used in developing an analytical model for transmission XRD by a casting

specimen encased by mold wall.

23
(K) of the coherent intensity is forward directed. It is this forward-directed scattering which will

produce the transmission XRD pattern. The entire second term in the summation thus gives the

fractional generation of coherent scattered radiation which emerges from a point within the

specimen in the forward direction. The value ofi^ is determined by the geometry of the

diffraction experiment. Since the pattern is observable only at the x-ray imager, we assume K is the fractional solid angle subtended by the imager from the point of scattering.

Equation (2) can be symbolically simplified to

I,{E) = /,(£) KN[e ''^'^'^'^' - e

t'^^^^^'^^^ ^ ^^^^^^^l]

. (28)

The intensity of the coherent x-rays which emerge from the exit mold wall is given by

I,iE) = I,{E) e'-'-''^'-''^^ , (29)

where

W2 is the thickness of the exit mold wall.

Combining eqs (26), (28), and (29) gives an expression for the intensity of coherent x-rays

emerging from the exit mold wall in terms of the thicknesses, the densities, and the x-ray

attenuation coefficients of the mold walls and specimen. It is convenient to compute the ratio

Ij(E)/Iq(E) which is the fraction of the incident x-rays which emerge in the forward direction, from

the mold-encased specimen, as coherent radiation.

3.1.1 Advantages and Limitations of the Attenuation-Coefficient Model

The simple model for transmission diffraction gives the correct energy dependence for small

scattering angles and can be used to compare diffraction efficiencies for variations of specimen

and mold thicknesses and densities. However, because the model does not account for the

constructive interference of coherent scatter from atoms in a crystalline solid, it cannot predict

intensities for reflections from particular lattice planes. For the same reason, the absolute

efficiencies are incorrect, and K is actually a flinction of the diffraction angle and energy.

3.1.2 Model Predictions for Metal Specimens

This simple model has proven useful for investigating transmission diffraction for the materials

we used in our experiments. The effects of specimen thickness, and of mold material surrounding

the specimen were studied extensively. Partial and total x-ray attenuation coefficients were

24
computed using the XCOM software package [22]. The value ofK was chosen as 0.007, being

representative of our laboratory XRD apparatus (imager 50 mm in diameter located 150 mm from

the diffracting specimen).

Figure 18 plots I/EJ/IgfE) for a specimen of pure aluminum. The efficiency of transmission

XRD is a strong function of both the specimen thickness and the incident x-ray energy. The

peaks in the plots indicate an optimal range (50 to 100 keV) of x-ray energies for transmission

XRD on these aluminum specimens. The optimum energy yields the highest intensity of diffracted

x-rays which are able to penetrate through the specimen.

Remember that plots such as shown in Figure 18 include the effects of both attenuation and

diffraction. For a thin specimen, there is very little attenuation. However, the irradiated volume

of a thin specimen does not generate much diffraction. A thicker specimen attenuates more of the

incident and diffracted x-rays, but produces a stronger diffraction pattern. For high-energy x-rays

and the range of aluminum thicknesses shown, diffraction dominates attenuation.

Figure 19 shows plots of model-generated efficiency of diffraction for a nickel specimen.

Because the mass attenuation coefficients and density of nickel are higher than those for

aluminum, the efficiency of transmission diffraction is lower. For specimens 2 to 10 mm thick,

diffraction again overwhelms attenuation. But for specimens of greater thickness (20 to 25 mm),

attenuation of the incident and diffracted x-rays begins to dominate and the efficiency of

diffraction decreases. Note also that the optimal x-ray energy for transmission diffraction is higher when a nickel specimen is probed than that for an aluminum specimen of identical

thickness.

3.1.3 Model Predictions for a Mold-Encased Specimen

Figure 20 shows plots of effiency of diffraction for a nickel specimen 10 mm thick sandwiched

between two pieces of mold material, each of the thickness indicated in the legend. Attenuation

coefficients for the mold material (a mixture of alumina, silica, and zirconia) were computed using

the XCOM software. The density of a sample of the material was 2.6 x lo^ kg/m^ . For x-ray

energies over 150 keV, even mold-wall thickness as large as 7.5 mm decrease the XRD intensity

only by about one-half

3.1.4 Modeling Various Fractions of Liquid and Solid

Anticipating that we would use the XRD technique to probe the "mushy" zone (area of

dendritic solidification containing both solid and molten material) of a casting, we modeled a specimen volume containing both liquid and solid. The liquid portion of the specimen was

assumed to attenuate the incident and diffracted x-ray beams. The correct (lower) density of the

liquid was used. The solid portion of the specimen attenuated both the incident and scattered x- rays as well and produced coherent scatter. A 6 mm thick section of casting was modeled, with

various fractions of the thickness being comprised of molten metal andcrystalline solid. Energies

25
7E-07 1

6E-07

5E-07

o

.§ 4E-07

SE

LUQ 3E-07

a:X

2E-07

1E-07

1 1 ! 1 1 1 _«_ 2 —^5 -^ 10 -^*-20-«-25 A - L\ Aluminum Thickness (mm)

l\\ ^

jf \'I \X vw K \\ \ VV

\ N\

\ ^3k^ k V ^^

'^^K-. V VX,^^^

-»^ ^

^*«*«-

'«»»HHS -a-sHSo*

jQjgQjijj bs^s&aaajssssst

^^

100 200 300

X-Ray Energy (keV)

400 500

Figure 18. Plots of model-generated XRX) efficiency from an aluminum specimen. The legend

gives the thickness, in the range 2 to 25 mm.

3E-07

^2E-07

c:o

LUQ

X 1E-07

1 1 1 1 1 1 _«^2 —^5 -^ 10-*.-20-«-25

Nickel Thickness (mm)

J % ^^ '' /

JrM

' V^.

"^^^

**S5

Uf V,-^ •--, -^

il 7?--^

'«».^immsum

'^^^^

'«-».^

*'»^«.*<». »Wi-5i^ ^~ 100 200 300

X-Ray Energy (keV)

400 500

Figure 19. Plots of model-generated XRD efficiency from a nickel specimen. The legend

gives the thicknesses, in the range 2 to 25 mm.

26
3E-07

^ 2E-07

c

0)o

LUQ

X 1E-07

1 1 1 1 1 1 1 1

--*- —^ 1 —^

2 -*- 5 -*- 7.5

Mold Wall Thickness (mm) 1

J ^

V

r

::::- fe^

{//

^^.^ *»«*, ^

SS

.M

"1*4

100 200 300

X-Ray Energy (keV)

400 500

Figure 20. Plots of model-generated XRD efficiency from a nickel specimen 10 mm thick

surrounded by mold material.

1.8E-07

1.5E-07

^1.2E-07

c

.0) £ 9E-08

Q

X 6E-08

3E-08

1

1 1 1

1 11

1 1 ^"

- -»- 0.167 —^ 0.333 -•- 0.500 -ste- 0.583 -*- 0.833 ^^ 1.000 —

-J^<

Solid Fraction f X

ir^^V

i/j,^\X V Xn::k.

N^jN>Sc ^2<::

^

*!S^

7

f^

^"^^ ^& ^

^fe; >»8a85^ -^"^.55^

' TMTM"*s«

»^^j^ft^ ^ig mmma^gamEaae ^MaSK^^^^^'^°T'^^^~^stBr^-

100 200 300

X-Ray Energy (keV)

400 500

Figure 21. Modeled efficiency of transmission XRD through a nickel-alloy specimen 6 mm thick.

Various fractions of the total thickness are modeled as liquid and crystalline solid.

27
in the range from 20 to 500 keV were considered. Figure 21 shows plots of the XRD efficiency

(fraction of the incident x-ray intensity which emerges as coherent radiation) as a function of the

x-ray energy. For low fractions of solid the efficiency of diffraction and the intensity of diffraction

spots are low. Efficiency and intensity increase as more of the specimen thickness is in a physical

form (crystal) which diffracts the incident x-ray beam. Figure 22a plots values of efficiency (from

Fig. 21) at several x-ray energies. Figure 22b plots these efficiencies, normalized to the efficiency

when the entire specimen is a single diffracting crystal (fraction of solid is 1). The relationship

between efficiency and fraction of solid departs only slightly from a linear one. The slightly concave shape of the curve results from differences between the densities of the liquid and solid.

1.4E-07 1

1.2E-07

1E-07

5^ 8E-08

6E-08

4E-08

2E-08

o

c

o

HIQ

crX

I-"" "T- \ \ _B»_ 100 -^- 150 -^- y 200 ^

^

X-Ray Energy (keV) y ' y ^

X

/^

of y -x^ jjp^ /^ ^

X

w y^

^Bsr^

y

*^ ^^

> y^^^r .^^^J^

ffl^^ •^<^

J^

^^ ^

0.2 0.4 0.6

Solid Fraction

0.8

1

-1 o

m^

5; n fl ^M^^

<u U.O

o ,^

^

U.O Q J m^ r

CD j^\ .^'

0) ^^^^

! y

0.2 0.4 0.6

Solid Fraction

0.8

Figure 22. Efficiency of transmission XRD, at several x-ray energies, through a nickel-alloy

specimen 6 mm thick. Various fractions of the total thickness are modeled as liquid

and crystalline solid. The plots in (a) are normalized in (b).

28
3.2 Fundamental Physics Model

We showed in section 2 that for a small single crystal, illuminated by an unpolarized x-ray

beam, the scattered intensity could be calculated. This intensity is not measureable, but the total

diffracted energy (integrated intensity) is. The total diffracted energy is given by

E = -^w R^ m^ c^

[l+cos^(29)]

2 sin(20)

1

471 e,

-) FF* e -IM A^il

(30)

where

o) is an angular rate of rotation of the specimen, required to insure that all area under the interference fiinctions, eq (22), has been integrated,

Fis the volume of a small segment of the specimen illuminated by the incident x-ray beam,

v^ is the volume of the unit cell of the crystal.

The coherent-scattering term in eq (27) can be replaced by eq (30). Attenuation in the mold and

casting, given in eqs (26), (27), and (29) remains the same. The energy-dependence of diffraction

comes into eq (30) through the energy-dependent atomic scattering factors which are included in the structure-factor term FF'^. The Lorentz-polarization factor term is also a function of x-ray

energy, through the scattering angle 26.

Figure 23 shows the efficiency of transmission XRD modeled by eqs (26), (27-modified),

(29), and (30), for the (111) reflection from nickel. The energy dependence is similar to that

shown in Figure 19. However, the absolute intensity is correct.

0.0014

0.0012 ^ 0.001

o

% 0.0008

Q 0.0006 ^ 0.0004

0.0002

1 1 1 1 1 1 1 -»- 2 -^5»- 5 --- 1 -«8r- 20 —^

25

1

^H L

^N,\y*.

. ^v** V.

^

]Ss%As l^^a&niM^ CH

/^ "^ ^*84s^

*>^^

^**«^

/ 1 f.^

^"^^

^^^ffltea.

-I 1 7^

\u V

H>«SU ^sss^sa—— ^isHm^ag

-J. JJ

100 200 300 400

X-Ray Energy (keV)

Figure 23. Plots of model-generated XRD efficiency from a nickel specimen.

500

29
4. APPARATUS

4.1 Equipment for High-Energy, Transmission Diffraction

Figure 24 illustrates the key elements in the apparatus used for transmission XRD

measurements. The x-ray tube produces a high-intensity, polychromatic source of x-rays

restricted by collimators to a small circular beam. A fraction of the x-rays interacting with the

sample is diffracted. An x-ray imager detects the x-ray pattern incident on its two-dimensionally

sensitive area. An energy-sensitive detector may instead be used, in place of the imager, to measure the spectra of the primary and diffracted x-rays.

The components of the diffraction system are described first, followed by descriptions of the

laboratory apparatus used for room temperature studies, and the furnaces used for melting and

solidificaton experiments. Three separate furnaces were assembled for our tests—a low

temperature test cell for melting gallium, a medium temperature gradient furnace for melting

aluminum and copper, and a high-temperature directional solidification furnace (for growing

single-crystal castings of nickel-alloy).

4.1.1 X-Ray Source

Two sources of x-rays were used in our experiments. Both were metal-ceramic, tungstenanode tubes with a beryllium exit window, intended for use in industrial radiographic imaging. A

160 kV tube head (Fig. 25) was used in early experiments. However, modeling indicated the need

for x-rays of higher energy when a turbine-blade casting was to be probed. A new x-ray tube

(Fig. 26) and high-tension transformer permitted experiments to be performed with tube potentials as high as 320 kV. An increased x-ray tube potential produces higher intensity characteristic

radiation lines and bremstrahlung spectrum, and adds new x-rays of higher energy which more

easily penetrate the mold-encased casting.

X-Ray

Source

Primary

Collimator

Diffracted

X-Rays

Secondary

Collimators

X-Ray

Imager

Specimen

Beamstop —

Figure 24. Components of the real-time, high-energy transmission diffraction apparatus.

30
Figure 25. End-window x-ray tube head, 160 kV maximum potential. A short collimator is attached to the tubehead.

Figure 26. X-ray tube head, 320 kV maximum potential. The collimator is shown affixed to the

tubehead in this photograph.

31
The choice of x-ray source diameter (focal spot size) of 1.2 mm or 4 mm (320 kV tubehead), or 0.2 or 3 mm (160 kV tubehead) is selected by activating one of the two filaments in the tube.

The small (1.2 mm) focal spot size of the 320 kV tubehead proved most useful in our experiments

because its size corresponds to the diameter (1 mm) of the collimating apertures. X-ray intensity

from this source v^as significantly higher at the specimen, by a factor of 10, than that obtainable

from the 0.2 mm source in the 160 kV tube head. The higher intensity yielded a higher signal-tonoise ratio in the XRD images.

Controls on the constant-potential x-ray generator permit x-ray tube voltages to be varied over the 15 kV to 320 kV range. A tube current of 3 mA is possible at 320 kV. For some

experiments a means for reducing the x-ray source intensity was required so the diffraction signals

did not overwhelm the detector system. A lower intensity was obtained by modifying the

controller. Tube currents as low as 0.05 mA with incremental changes of 0.05 mA were possible.

A pinhole-camera image of the x-ray source (focal spot) was be made by placing a small (0.5

mm diameter) aperture in a lead plate between the x-ray tube and an imaging device. The

dimensions of the source and its uniformity can be assessed from the image. Figure 27 shows an image produced by the 1.2 mm diameter focal spot of the 320 kV tubehead.

Figure 27. Pinhole camera image of the 1.2 mm diameter focal spot of the 320 kV tubehead.

X-ray parameters were 320 kV, 1 mA.

32
4.1.2 Leakage Radiation and Supplemental Shielding

During experiments with a high-sensitivity x-ray detector, the presence of undiffracted

radiation was evident. An investigation was made to determine the source of the unwanted

radiation. An x-ray pinhole camera was constructed (with lead walls 10 mm thick and a pinhole 2

mm diameter) to image the location of the radiation leaking from the x-ray tube housing. An

electronic x-ray imaging device was used to provide a real-time image of any undesirable radiation sources within the field of view of the pinhole camera. X-rays were found to be leaking from the area surrounding the collimator (Fig. 28). Supplemental x-ray tube shielding (lead, 9.5 mm thick),

alleviated the leakage radiation problem and improved the signal-to-noise ratio of the diffraction

images.

4.1.3 Collimators

A beam-restricting collimator (Fig. 29) was designed and fabricated. A triple-aperture design

(Fig. 1) was employed to minimize beam divergence and optimize x-ray intensity [24].

Interchangeable sets of 9 mm thick lead disks can be used to select beam diameters of 0.3 mm,

1 mm, 1.5 mm, or 2 mm. An alignment laser, placed in an opening in the base of the collimator,

projects a visible beam along the same path as that of the x-ray beam. This permitted fast, safe,

and simple alignment of the beam-stop and specimen.

Figure 28. X-ray pinhole camera image of radiation leakage from the 320 kV tubehead.

33
Lead

Aperture

Figure 29. Drawing of the collimator which restricts the x-ray beam to 1 mm diameter.

4.1.4 Beamstop

The primary beam transmitted through the specimen is often of high intensity. Blocking this

beam from the detector improves the contrast of images and prevents an energy-sensitive detector

from being overwhelmed by high count rates. A small tungsten rod (4 mm diameter and 6 mm

thick) was positioned in the center of the primary x-ray beam emerging from the specimen, to act as a beamstop. X-rays diffracted from the sample pass to the sides of the beamstop and are imaged, while the undififracted primary beam is severely attenuated. The tungsten disk was

suspended by a graphite/epoxy composite support (Fig. 30). The low attenuation in the

composite minimizes the shadow it casts on the x-ray images.

4.1.5 X-Ray Imager

An instant-process film was used as the x-ray detector for our first experiments. The film

could be positioned to intercept various portions of the x-ray scattering from the sample.

Exposure times of less than one minute were sufficient to record discemable diffraction patterns

when x-ray source parameters of 75 kV and 18.5 mA were used.

;v^

Figure 30. Tungsten-rod beamstop supported by a graphite/epoxy wand.

34
A real-time x-ray imager, designed specifically for x-ray diffraction, was acquired and used for

all experiments reported in this paper. This unit (Fig. 3 1) uses a scintillator screen, coupled to an image intensifier, which is then coupled to a charge-coupled device (CCD) camera sensitive to low light levels. Fiber-optic coupling between the scintillator, image intensifier, and CCD camera

transfers light extremely efficiently. Image intensifier and video gain were adjustable. The imager

was originally equipped with a 70 |im thick gadolinium oxysulfide (Gd202S) scintillator, resulting

in a system with a resolution of approximately 80 fim. The field of view of the imager is approximately 40 mm wide by 30 mm high. Imager specifications are summarized in Table 1.

Table 1 . Specifications for the real-time x-ray crystallography imager.

Scintillator

Input image size

Optical coupling

Video format

Video output

Gain range

Physical size

70 |am thick polycrystalline gadolinium

oxysulfide

50 mm diagonal, 3:4 aspect ratio

Fiber optic throughout

CCIR 625 lines at 50 Hz

1 V peak-to-peak into 75 Q

1 to 1000, user adjustable

287 mm L, 80 mm H, 107 mm W

Figure 3 1 . Real-time x-ray imaging device. The imager comprises a scintillator, image intensifier,

and a CCD camera.

35
We used a calibration grid (5 mm line spacing) fabricated from thin copper-coated printedcircuit-board material to measure the spatial uniformity of the imager. The grid was affixed to the

front of the scintillator and placed in a low-intensity x-ray field. Figure 32 shows the resultant

image. Note the pincushion distortion of the grid. The spatial distortion in a recorded diffraction

image can be corrected by reference to the calibration image.

To improve the signal-to-noise ratio of the XRD images, we examined the efficiency of the x- ray imager. To be detected, diffi-acted x-rays must be absorbed in the scintillating layer at the

front of the imager and produce light. The scintillator material and its thickness determine what

fraction of the incident x-ray flux is absorbed. There is a tradeoff between good spatial resolution

with a thin layer and high absorption in a thick layer. The x-ray imager (with the gadolinium

oxysulfide scintillator) was optimized for high spatial resolution at low to moderate energies. As

we pushed the x-ray energy in our experiments ever higher for increased transmission through

furnace components, mold, and specimen, the efficiency of the imager decreased. Although

acceptable transmission XRD images could be obtained, an improvement was possible by

replacing the gadolinium oxysulfide scintillator with one having a higher attenuation at energies up

to 320 keV. A 6 mm thick fiber-optic glass scintillator [27], which had been acquired for work at 160 keV, was affixed to our imager. The fiber-optic scintillator produces extremely low lateral spread of light and high-efficiency transfer of light to the image intensifier. Figure 33 shows the

absorption calculated for the scintillators. The glass scintillator absorbs a much greater number of

x-ray photons than the gadolinium oxysulfide, particularly at high energies.

iff^

^^^^-ft^rfe

Figure 32. Image of the calibration grid (5 mm line spacing) showing pincushion distortion

inherent in the x-ray imager.

36
c

uuyo

1 ^

V

80%- \\V

fin%

\

DU /o v^x^

t \

^^ 1 3 nmi thick Ge detector

4no/„ - A \V . 'fU /o \ \ \ 6 mm thick scintillating glass

20%- V \> S V

' ^s.— : 70 micron thick gadolinium oxysulfuide

n%- \ 100 200 300

X-Ray Energy (keV)

400 500

Figure 33. Absorption of x-rays in the 70 ^m thick gadolinium oxysulfide scintillator and the 6

mm thick fiber optic scintillator. For comparison, the absorption in our energysensitive germanium detector is shown. The discontinuity at 50.2 keV in the curve for

gadolinium oxysulfide occurs at the K absorption edge of gadolinium.

Acquisition and storage of the video frames from the PAL-format imager is performed with an

eight-bit, monochrome frame grabber installed in a personal computer. A coprocessor board,

connected to the frame grabber, speeded image manipulations and frame averaging (to increase

signal-to-noise ratio). Frame averaging could be performed at a rate of 25 frames per second.

Image acquisition and processing software provided the ability to perform dynamic range

expansion and compression, image averaging, and image subtraction, as well as image filtering to enhance the acquired images.

A muhiformat video cassette recorder was used to record radiographic and diffraction images

during all experiments. This served as a backup for direct image acquisition with the frame

grabber, and was useful in cases where the image was rapidly changing (dynamic events such as mold filling). Video frames could be digitized after the experiments by replaying the video tape

through the frame grabber. The image degraded almost imperceptibly compared with the image

acquired directly from the x-ray imager.

4.1.6 Energy-Sensitive Detector System

In addition to x-ray diffraction images, we have investigated the use of energy-sensitive

detectors. The diffraction interaction is an energy as well as spatial filter. An x-ray imager placed

in the diffraction field records the spatial location of diffracted x-rays. An energy-sensitive

37
detector placed at the same location as the imager would record energy peaks associated with

each of the diffraction spots. To explore the information contained in the energy spectrum of

diffracted x-rays, we began to use an energy-sensitive x-ray detector. Preliminary experiments

using a large (75 x 75 mm) Nal scintillator appeared promising; however, the poor energy

resolution precluded observing the expected spectral peaks.

An improved system (Fig. 34) includes an intrinsic germanium detector with an integral field- effect-transistor preamplifier, a high-voltage detector bias supply, a linear amplifier, and a multichannel analyzer. The germanium detector was a thick, large-area planar type. Components

of the system were optimized for high sensitivity in the 40 to 500 keV range and high counting

rate (2 x lOVs) capability. Specifications for this equipment is given in Table 2. For some

experiments, a collimator was placed in front of the germanium detector. This permitted

examining the energy spectrum of smaller areas (less than 36 mm diameter) in the diffraction field.

4.2 Laboratory XRD Apparatus

The x-ray source collimator, sample, beamstop, and x-ray imager were assembled as shown in

Figure 35. The specimen was placed in the collimated x-ray beam using a versatile fixture. Both

the imager and the fiamace were on separate rotating stages. The imager stage could be

manipulated under computer control. The furnace could be raised and lowered remotely, as well.

The furnace and imager were also attached to roller-bearing stages so that the x-ray source-tosample distance could be varied, and the furnace could be moved side-to-side in the x-ray beam.

The fixture rigidly supported the x-ray source, sample and x-ray imager, and had provisions for

quantitatively determining positions and angulations.

Germanium

Detector

Spectroscopy

Amplifier

Personal

Computer

Figure 34. Energy-sensitive detector system. The components were optimized for extreme

counting-rates, so high-intensity areas in the x-ray field could be evaluated.

38
Table 2. Specifications for the energy-sensitive x-ray detector system.

Detector type

Detector dimensions

Detector bias

Detector energy resolution

Amplifier

Multichannel analyzer

Intrinsic germanium, planar geometry

36 mm diameter x 13 mm thick

1500 Volts, negative polarity

0.332 keV at 5.9 keV, 6 |is shaping time,

0.573 keV at 122 keV, 6 |is shaping time,

0.754 keV at 122 keV, 1 ^s shaping time,

and count rate of 1 0^ s"^

Linear spectroscopy amplifier, 2.5 to 1500

gain, 0.5 to 10 \is shaping times, pulse pileup rejector, automatic pole-zero adjustment,

baseline restorer

16384 channels, (2^^-l) counts per channel,

counting rate throughput >10^ s"\ PC-based

interface for control and data transfer

Single Crystal

Diffracted

X-Rays

Collimated

X-Ray Beam

X-Ray

Imager

Collimator

Figure 35. Drawing of the laboratory apparatus used for XRD experiments at room temperature.

39
4.3 Gallium Test Cell

It was convenient to begin our diffraction experiments with gallium. Its low (28 °C) melting

point permitted studies to be made close to room temperature, and the large (3 percent) change in

density between the solid and liquid was great enough to produce a discernable difference in

brightness on a radiographic image. The ability to independently determine the position of the

liquid-solid boundary (brighter versus darker areas of the radiograph) provided a means for

validating the spatial performance of the XRD sensor. A container (Fig. 36) was fabricated from polymethylmethacrylate. A temperature gradient

could be established between the °C temperature (ice) at the top of the cell and an electrically

heated region lower in the cell. A temperature controller connected to the heater produced a

steady-state boundary between solid and liquid gallium. The lower-density solid is at the top of

the test cell. The position of the probing x-ray beam could be moved into the solid or liquid by a remotely controlled positioning fixture. We could switch between the XRD sensor and

radiographic imager without changing position by removing the coUimating apertures in the x-ray

beam.

Solid -

Gallium

Heater /

Ice

Liquid-Solid

Boundary

Acrylic

Plastic

Fixture

Figure 36. Gallium test cell. A steady-state boundary between solid and liquid could be

established by controlling the heating element.

40
4.4 Medium-Temperature, Gradient Furnace

Since the aim of developing the x-ray diffraction technology was to study metal solidification, a furnace was required to heat and melt the specimen. Figure 37 shows the controlled-gradient

furnace. It is a vertical tube furnace with separate controls for both the upper and lower regions

of the tube. By adjusting the temperatures of the two zones, a temperature gradient could be

established for solidification in the region of the furnace probed by a collimated x-ray beam. The

specimen to be melted was placed in a closed-end quartz tube (25 mm i.d., 2.2 mm wall thickness,

300 mm length). The type K thermocouples used for temperature measurement and control were

protected by closed-end quartz tubes 1 mm i.d., 28 mm long. The flirnace was designed to reach

1100 °C. It has been tested to 1100 °C and has proven suitable for controlled melting and

solidification of aluminum and copper. We have repeatedly cycled through the temperature range

within which the metal sample melts and solidifies.

The solidification zone of the gradient furnace is established by adjusting the temperature of

the upper heater to be above the metal-melting point and that of the lower heater below the

melting point of the specimen. Normally, the liquid-solid boundary is positioned within the area occupied by the ceramic foam spacer. The foam spacer provides a path of low attenuation for the

probing x-ray beam.

Ceramic-Fiber

Insulated Heaters

Molten/Solid

Metal Specimen

Type K Thermocouples

Protected by Quartz

Capillaries

Alumina-Foam Spacer

Quartz Specimen

Container

Alumina-Foam End Caps

Figure 37. Gradient furnace for melting and solidification studies of aluminum and copper.

41
In our melting experiments on aluminum and copper, the metal was enclosed in a quartz tube.

At the elevated temperatures in the gradient furnace (700 °C for aluminum and 1 100 °C for

copper) the metal reacted with the tube, scavenging elements from it. Additionally, because of

the difference in thermal contraction of the metal and quartz, the tube often cracked upon

cooling. To alleviate these two problems, the specimen receptacle was changed to graphite,

which was less reactive with the metals and more tolerant of thermal cycling. However, the

graphite crucible cannot be used in an oxygen environment because of the possibility of

oxidation and fire. Therefore, a glass enclosure was designed and built so the gradient furnace

could be flooded with inert gas. The additional borosilicate glass of the enclosure walls (3 mm

thick) did not appreciably alter the x-ray diffraction images obtained.

4.5 Directional-Solidification Furnace

A resistively heated directional-solidification (DS) furnace (Fig. 38) was acquired. The

vacuum furnace (100 mm bore) was capable of producing 1700 °C temperatures. The x-ray source (A) and collimator (B) are on the far right. The small-diameter x-ray beam passes through

a borosilicate glass port 10 mm thick into the furnace. The beam then encounters molybdenum

resistance-heater windings (D) of 1.6 mm diameter. The wire is wound on an aluminum oxide

support tube (E) (100 mm ID, 4.5 mm wall thickness). After passing through the coil support,

the x-ray beam enters the casting mold (F) (6.4 mm wall thickness). The cavity of the mold for

the first melting experiment was 3 mm thick by 38 mm wide (producing a thin rectangular bar).

The exit path x-rays, after diffraction from the specimen, was through 6.4 mm of mold, 4.5 mm of

alumina, 1.6 mm of molybdenum, and 10 mm of glass. The real-time x-ray imager (G) was

positioned outside the glass port to intercept the diffracted x-rays. The specimen was 780 mm

from the x-ray source and 400 mm from the imager. We took advantage of the asymmetry in the

location of the hot zone of the furnace within the bell jar, by placing the imager nearest the

specimen. This shorter distance, from specimen to imager, yields a larger angular field of view.

The x-ray source and imager were attached to two-axis motion stages. The source and

imager could be scanned in unison (horizontally and/or vertically) to probe different regions of the

specimen. However, by leaving the x-ray source fixed and scanning the imager, a large virtual

field of view was achieved. The system is capable of moving the 130 kg x-ray head in

submillimeter increments and at speeds more than sufficient for following the liquid-solid

boundary in a DS casting. An early test, with no specimen in the furnace, disclosed that the

primary x-ray beam intensity at the imager was not high enough to damage the imager.

Therefore, no beamstop was required in these diffraction experiments. The large bright spot

visible in many of the XRD images from furnace experiments is the primary x-ray beam.

Enclosures for radiation shielding were fabricated, from 16 mm thick steel around the x-ray

tube and 9.5 mm thick steel around the x-ray imager. Additional shielding was provided by lining

the enclosures with lead sheet. Radiation surveys near the furnace indicate that the researchers can safely occupy areas near the flirnace during operation of the XRD system.

42
A - X-Ray Source B - Collimator C - Boroslllcate Glass Port D - Mo Windings E - Alumina Coll Form

F - Mold G - X-Ray Imager

Figure 38. Configuration of tlie directional-solidification furnace fitted with the XRD equipment.

The dashed lines indicate lead-lined steel enclosures used for radiation shielding.

In normal operation, a mold containing a metal charge in a crucible at its top is placed in the

load chamber of the furnace. After a 10 |im vaccum has been established the gate valve is opened

and the vertical ram raises the mold into the hot zone of the furnace. The alloy charge melts,

filling the mold. Solidification initiates at the base of the mold where the alloy contacts the watercooled ram. The mold is slowly (150 mm/hr) withdrawn through the steep temperature gradient

established between the hot zone and a chill plate beneath it. A single-crystal casting is produced.

Figure 39 shows a mold typical of that used in the single-crystal casting experiments. The

mold is fabricated by repeatedly coating a wax replica of the part to be cast with a slurry of

refractory oxides (alumina, silica, and zirconia). The slurry used for initial coats is very fine, to produce a smooth inner coating. The slurry for outer coats is increasingly coarse. The outer

surface of our molds had an rms roughness of about 2 mm. Roughness varied from mold to mold.

Once the requisite mold thickness has been achieved, the wax replica is removed by heating the

mold. The mold is then baked at high temperature to harden it. To study different effects, we

used molds with circular, triangular, or rectangular cross sections (Fig. 40).

During casting experiments, a metal alloy charge is placed in the crucible. When the mold is raised into the hot zone of the furnace, the alloy melts and flows into the mold. The alloy

solidifies as polycrystals (grains) in the starter block. The fastest-growing grain reaches the grain

selector (a corkscrew shaped section of the mold) first and blocks growth of all other crystals

with differing orientation. If the thermal conditions are correct, growth of a single-crystal

continues upward in the mold as the mold is slowly withdrawn through the furnace.

43
^

I Crucible p

Cavity

for Producing

Casting

Flat Base

sits on chilled

furnace ram\^

Refractory

Oxide

Mold

Grain

Selector

^^

Starter

I I Block

Figure 39. Side view of a typical investment casting mold used for producing single-crystal

castings.

015.5

i

3.2 J

24.6

V/////////////^^^

6.4-"

Figure 40. Cross sections of the four types of molds used in our casting experiments. All

dimensions are in mm.

44
4.5.1 Modifications to the DS Furnace

The geometry of x-ray source, specimen, and x-ray imager for the tests in the directional

solidification flirnace was very different from that of the moderate-temperature XRD apparatus.

The diffracted x-ray intensity arriving at the x-ray imager is much lower because the distance

between the x-ray source and imager is much larger, and there is a great deal of attenuation from

the many additional materials encountered along the x-ray path through the furnace. Figure 41

shows a cross section of the furnace as it was configured when received.

Initial experiments with the DS furnace indicated that the region of solidification in the casting

was beneath the field of view of the XRD sensor. The hot zone of the furnace had to be turned

off after melting occurred, to drive the solidification upward into the region probed by the sensor. To correct this problem, we rearranged components in the furnace and added new elements.

The hot zone (alumina core with molybdenum windings) of the furnace sat directly on the chill plate. Solidification occurred at the location of the chill plate or below it. This area is inaccessible for XRD because of the locations of the diffusion pump inlet, the chill plate, and its cooling coils. A 38 mm thick piece of alumina foam was used as a spacer between the chill plate

and the hot zone. The foam has a structural rigidity sufficient to support the hot zone, but a

density (240 kg-m*^) low enough to provide good x-ray transmission. At the same time the foam

spacer was added, the chill coils were raised slightly. This was done to preserve the high

temperature gradient in the furnace which drives solidification in the vertical direction.

Extension of the top of the metal bell jar was required to raise the hot zone. Figure 42 shows

the section added to the bell jar. Cooling coils were soldered to the extension to prevent

overheating.

We have made further modifications to the directional solidification fijrnace. These changes were made to shift the solidification zone in the casting to coincide with the field of view of our XRD sensor (x-ray source and imager) and to enlarge the region of the casting we could

Metal

Bell Jar

X-Ray

Imager

X-Ray

Source

Figure 41. Side view of the bell jar in the directional solidification furnace as it was configured

when received.

45
Bell-Jar

Extension

Low-Density

Alumina

Foam

Figure 42. Side view of the bell jar in the directional solidification fUrnace after recent

modifications.

investigate. Figure 43 shows a cross section of the furnace after the latest modifications. The

height of the alumina foam spacer was increased from 38 mm (previous modification, Fig. 42) to 60 mm, thus enlarging the vertical range we could probe with the x-ray sensor.

Graphite-Epoxy

Vacuum

Port

\

c^

r

Hot Zone

. Low-Density

Alumina

Foam

9 fl^=^

Graphite-Epoxy

Vacuum —j

Port /

498

869

/

Figure 43. Side view of the bell jar in the directional solidification flirnace after the final modifications to enlarge the field of view for XRD.

46
The ceramic foam spacer, beneath the hot zone, provides a path of low x-ray attenuation, free

of interfering structures. The chilling coils were lowered slightly below the chilled plate. New

support feet (fabricated from alumina foam) were constructed, to drop the top of the chilled plate

to the height of the diffusion-pump inlet.

The added height of the hot zone of the furnace above the baseplate necessitated construction

of a spacer (with water-cooled passages) for the vertical ram. The casting mold was then able to be positioned as before, vertically centered within the hot zone of the furnace.

The alignment of the crystalline planes in the casting can vary rotationally about the axis of the

casting and can deviate from the vertical axis. A means for orienting the probing x-ray beam to obtain strong diffraction spots was devised. The vertical ram of the furnace was altered to permit

rotation of the mold (and specimen). The rotation allows us to position the solidifying metal such

that Bragg conditions are satisfied and diffraction spots can be observed. After the specimen

rotation capability was added to the furnace (in August 1996) strong diffraction patterns from the

crystalline alloy castings could be obtained during every experiment.

4.5.1.1 Modeling of Transmission XRD From a Casting in a Directional-Solidiflcation

Furnace

Our XRD model was used to predict the efficiency of the transmission XRD process for

studying soHdification of a specimen within the high-temperature directional-solidification furnace.

Modeling (Fig. 44) shows the advantage which can be achieved if the hot zone components

(alumina core and molybdenum windings) can be removed from the path of the XRD sensor. An

additional increase in diffracted intensity can be expected if the borosilicate glass ports of the

fiirnace are replaced with low attenuation graphite epoxy ports.

We had ports 9.5 mm thick fabricated from a graphite epoxy composite (quasiisotropic layup).

The high modulus of the composite makes it ideal for a vacuum port, and the very low atomic

numbers and densities of the fiber and matrix exhibit extremely low x-ray attenuation. Less of the

incident and diffracted x-ray beams are attenuated in the ports, yielding a higher diffraction spot

brightness. X-ray transmission was measured to assess the improvement in transmission due to use of the new graphite/epoxy ports. The two new ports attenuated the beam by only 15 percent,

as opposed to the 44 percent attenuation by the glass ports (an improvement of a factor of 1.5).

4.6 Radiation Safety

Radiation shielding for our x-ray diffraction facilities was considered before begining any of

the experiments. The reflection XRD, laboratory XRD, gallium test cell, and the mediumtemperature gradient furnace studies were performed in a lead-shielded room. The experiments

with the directional solidification furnace required adding radiation shielding around the source,

the imager, and along the beam path through the furnace. An enclosure made of steel plate for

the x-ray tube (16 mm thick) and for the x-ray imager (9.5 mm thick) provided adequate

47
shielding. A researcher could safely occupy the area near the furnace during XRD tests (Fig. 45

and Table 3). The low radiation dosages are largely a result of the extremely small (1 mm

diameter) x-ray beam used to probe the casting.

3.5E-08

3E-08

^2.5E-08

o

§ 2E-08

LUQ 1.5E-08

01

X

1E-08

5E-09

/"^V mold & specimen

/

f \ y

^ / \^ no hot zone - / \ ^ / NV / no 1\Kc\ /

. y >v /

/ J

^ ^N//

/

^^k^ 7^N,^^^

/// "^^^^:^^

^*^

^.^^^^

/// ^^^"^^

1 //

_^

,.^^—^ ^-^*^^^ 1 /

//

^^ "" « ^• J

/// /^ v\ ^-*^

//r J. ut \

\

\

\ 100 200 300

X-Ray Energy (keV)

400 500

Figure 44. Predicted efficiency of transmission XRD versus x-ray energy for a 3 mm thick N5

nickel alloy specimen encased in a refractory oxide mold (6.4 mm wall thickness). The

furnace ports are 10 mm thick borosilicate glass. The hot zone comprises an alumina

core with 4.5 mm thick walls and molybdenum windings (1.6 mm diameter wire).

48

ce

•cX

0)c

.2O

ctiI X

&0c

•c3

(UOaBac

.2'*-> o • oCo

(L> c

<u

Ui3t/3 O

cxX

(L) co1

(U "3OU

enH

T3 5 "^

ra rv 1

H-1 prjo ,

^5Ioo

as o — vo

00 o o o 0^ oo

ON o o o o o —

d d d d d d d d d d d d ddd rn

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5. DIFFRACTION EXPERIMENTS

Diffraction of high-energy x-rays was investigated experimentally, first by performing tests on

well-characterized single-crystal specimens. Effects on the diffraction pattern of materials

surrounding the specimen were studied and later, melting and solidification studies were

performed. The first melting experiments on pure metals with low melting temperature

demonstrated the feasibility of the diffraction technique. Next, aluminum and copper were studied

in a medium-temperature test cell. Finally, the transmission x-ray diffraction method was tested on castings of nickel alloy in a directional solidification furnace.

5.1 Back-Reflection Laue Images

The first experiments verified that x-ray diffraction could be obtained using our equipment.

We set up an apparatus typically used to form a Laue back reflection image. Our 160 kV

tubehead was fitted with 1.5 mm diameter collimators, and the beam directed through an instantprocess film cassette toward a piece of single-crystal turbine-blade casting. The source-tospecimen distance was 130 mm and the cassette was placed 30 mm from the specimen. With x- ray technique factors of 30 kV and 1 mA, the image shown in Figure 46 was formed after an exposure of 30 min.

Figure 46. Back-reflection Laue image (30 kV, 2 mA) of a single-crystal nickel-alloy casting

specimen.

51
5.2 Reflection XRD Experiments

An x-ray beam, collimated to 2 mm diameter, was inclined at 45° with respect to one face of a

single-crystal nickel-alloy casting (Fig. 47). The x-ray imager was also inclined at 45°, to give an

angle of 90° (20) between the x-ray beam and imager. A definite x-ray diffraction pattern was

obtained using a 50 kV x-ray tube voltage. The x-ray tube voltage was increased first to 75 kV,

then to 100 kV and finally to 160 kV. The diffraction pattern persisted, with a very noticeable

increase in intensity. The Compton-scattering background increased somewhat as tube voltage

was increased. This experiment verified that x-ray diffraction could be obtained with tube

voltages (160 kV) substantially higher than those used for conventional Laue measurements (40

kV).

We placed mold material 7 mm thick (typical of that used for turbine-blade castings) in the x- ray path during another reflection diffraction experiment. Figure 48 shows the recorded

diffraction patterns without (a) and with (b) mold material. The diffraction spot intensity

decreased with the mold present; however, the diffraction pattern was still discernable. No new

diffraction spots arising from the mold were noted. Compton scatter, observable in the images of

both the specmen alone and the specimen with mold material, diminished image contrast.

5.3 Transmission XRD

During reflection XRD experiments, the angles of incidence and scattering were varied to study the effects of angle on diffracted intensity. In one experiment on a thin single crystal of

copper, a transmission geometry was used. The diffraction spots were of high intensity, and the

Compton background was low. We quickly confirmed that a transmission geometry would permit

probing the interior of an object.

Figure 47. Reflection x-ray diffraction experiment. The x-ray source, specimen, and imager are shown.

52
Figure 48. Reflection x-ray diffraction pattern (160 kV, 1 mA, 20 = 90 °) from (a) a nickel-alloy

single-crystal specimen alone and (b) from the specimen, with a 7 mm thick piece of

mold material placed between the x-ray source and the specimen.

53
5.3.1 Single-Crystal Specimen

An experiment was performed on a single crystal of sodium chloride 12 mm thick, to verify

that transmission x-ray diffraction could be obtained on a thick specimen with high x-ray energies.

The x-ray beam (320 kV, 3 mA), coUimated to 1 mm in diameter, was directed along the [001]

crystallographic axis. A source-specimen distance of 270 mm and a specimen-to-imager distance

of 152 mm were used. Figure 49 shows the recorded transmission x-ray diffraction pattern. The

central round dark area in the center is the shadow of the beamstop. The bright diffraction spots

in the square array confirm the cubic structure of the sodium chloride crystal. Compare the image

with the standard (001) projection of a cubic crystal shown in Figure 50. Although 256 video

frames were averaged to achieve the high signal-to-noise ratio for this image, a single video frame

still clearly showed the diffraction pattern.

5.3.2 Determining Diffraction Spot Intensity

The intensities of diffraction spots for the transmission XRD experiments were measured by

defining a region of interest (ROI) surrounding each spot. Figure 51 shows the transmission

diffraction pattern of a nickel-alloy single-crystal with four ROIs. ROI-2 is the area of

transmission through the tungsten beamstop; it contains the primary broad-spectrum x-ray beam

attenuated by the specimen and beamstop. The other ROIs are centered on diffraction spots from

the specimen. Profiles were plotted through the center of each spot. Adjacent lines of pixels

about the profile line were averaged to improve statistics. The maximum gray level was

determined from the peak in the profile, and the background gray level was subtracted (Fig. 52) to give the peak intensity. A mean gray level was often computed as well.

Figure 49. Transmission x-ray diffraction pattern (320 kV, 3 mA) from a 12 mm thick sodium

chloride crystal. The x-ray beam was aligned along the [001] axis of the crystal.

54
100 Figure 50. Standard (001) stereographic projection of a cubic crystal. The numbers are the Miller

indices of the lattice planes.

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(ROI) identified. Gray-level profiles through these ROIs are also shown.

55
5.3.3 XRD Experiments on a Single Crystal Surrounded by Amorphous,

Textured, and Crystalline Materials

Transmission x-ray diffraction experiments were performed on a piece of single-crystal

turbine-blade casting 6.2 mm thick. Since the goal our research was to investigate metals during

the casting process, various materials were placed in the x-ray path during the diffraction

experiment, to confirm the ability to sense specimen structure through materials external to it.

5.3.3.1 Diffraction Experiment on the Nickel-Alloy Single-Crystal and Ceramic Mold

The nickel-alloy single-crystal was placed in the laboratory XRD apparatus. Figure 53 shows

transmission XRD patterns (320 kV, 3 mA) of (a) the specimen, (b) the specimen with 12 mm of

mold material (used for turbine-blade castings) placed between the x-ray source and specimen, (c)

the specimen with mold material placed between it and the x-ray imager, (d) mold material on

both the entrance and exit sides of the specimen, (e) a 12 mm thick slab of mold material, and (f) the two 12 mm thick slabs of mold material. The outer diffraction spots were apparently of low

energy and were thus strongly attenuated by the mold material. The inner spots, apparently of

high energy, were only weakly attenuated by the mold material.

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56
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Regions of interest were defined around each diffraction spot, and the spot intensity was

measured as described in section 5.3.2. The relative change in spot intensity is plotted as a

fiinction of mold thickness in Figure 54. The two slabs of mold material only decreased the

relative diffraction spot intensity to 0.6. This XRD experiment showed that even though the mold

material may have a distinct diffraction pattern (arising from the coarse granular structure on the

outside surface of the mold) the strong diffraction spots from the single-crystal nickel-alloy

specimen dominate the XRD image. Even when the material surrounding the specimen is very

coarse grained and relatively thick, the diffraction pattern from the specimen was observable. The

brightness of mold and specimen diffraction spots depends on the sizes of crystallites encountered

along the x-ray path, the orientation of the crystallites, and the structure factors of these materials.

5.3.3.2 Diffraction Experiment on the Nickel-Alloy Single-Crystal Surrounded by FineGrained Aluminum Plates

The nickel-alloy single-crystal was left undisturbed (same orientation with respect to the

collimated x-ray beam). Polycrystalline aluminum plates (15.4 mm thick) were placed on the

entrance and exit sides of the specimen. Transmission XRD patterns (Fig. 55) were recorded for

(a) the nickel-alloy specimen alone, (b) for the specimen sandwiched between two 15.4 mm thick

aluminum plates, (c) for the entrance aluminum plate alone, and (d) the both aluminum plates.

Note that the diffraction pattern from the nickel-alloy specimen surrounded by the aluminum is only diminished somewhat in intensity, with little or no interference from the diffraction patterns

from the fine-grained aluminum plates. Furnace walls of any material of low atomic number

should provide little interference in detecting the XRD pattern from a single-crystal nickel casting.

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Figure 54. Relative change in diffraction spot intensity from a nickel-alloy single crystal as a function of the mold wall thickness.

58
(a) Cb)

(c) (d)

Figure 55. Transmission XRD patterns (320 kV, 3 mA) for combinations of a nickel-alloy single

crystal and polycrystalline aluminum plates, (a) the nickel-alloy specimen alone, (b)

for the specimen sandwiched between two 15.4 mm thick aluminum plates, (c) for the

entrance aluminum plate alone, and (d) the both aluminum plates.

5.3.3.3 Diffraction Experiment on the Nickel-Alloy Single-Crystal Surrounded by CoarseGrained Metal Material

Transmission x-ray diffraction was again performed on the nickel-alloy single-crystal. A

coarse-grained aluminum rod 22 mm in diameter was placed on the entrance and the exit sides of

the specimen, to determine the influence of surroundings having a distinct diffraction pattern on

the XRD pattern of the nickel-alloy specimen. Figure 56 shows the four transmission diffraction

patterns obtained from (a) the nickel-alloy specimen, (b) the specimen with aluminum rod placed on the entrance side, (c) the specimen with the aluminum rod placed on the exit side, and (d)

aluminum rod alone. The transmission diffraction pattern of the nickel-alloy specimen still dominates the image; however, several high-intensity diffraction spots from the coarse-grained

rod are evident. Coarse-grained material surrounding the specimen may cause some interference;

however, the XRD pattern from the single-crystal nickel-alloy specimen is still clearly visible.

59
(a) (b)

(c) (d)

Figure 56. Transmission XRD patterns (SlOkV, 3 mA) for combinations of the nickel-alloy

single-crystal and a coarse-grained aluminum rod. (a) the nickel-alloy specimen, (b)

the specimen with aluminum rod placed on the entrance side, (c) the specimen with the

aluminum rod placed on the exit side, and (d) aluminum rod alone.

5.4 XRD to Determine the Physical State of a Specimen

5.4.1 Liquid-Solid Boundary in Gallium

Our investigations to demonstrate the feasibility of performing transmission XRD on a specimen (contained in a mold) to determine its physical state (solid or liquid) began with a

gallium specimen. Its properties permitted an independent confirmation of the physical state of

the specimen. Gallium exhibits a change (3 percent) in density between the solid and liquid states,

large enough to produce a discernible difference in brightness on a radiographic image. The

ability to independently determine the position of the liquid-solid boundary (brighter versus darker

areas of the radiograph) provides a means for validating the spatial performance of the XRD

sensor.

60
The test cell shown in Figure 57 was used for the gallium experiments. A steady-state

boundary was produced between the solid gallium (at the top because of its lower density) and the

liquid gallium. The position of the probing x-ray beam could be moved into the solid or liquid.

We could switch between XRD and radiographic imaging modes by removing the collimating

apertures from the x-ray beam. Figure 58 shows radiographic and XRD images with the x-ray

beam positioned (a) in the solid, (b) on the solid-liquid boundary, and (c) fully in the liquid

gallium. The circular black area in the center of each radiographic image is the shadow cast by

the tungsten beamstop. The x-ray beam is centered on the beamstop, so the dark area shows the

position of the incident x-ray beam.

When the x-ray beam was positioned to probe only the solid gallium, bright diffraction spots were observed. In the liquid, a diffuse ring of scattering was visible. At intermediate locations

between liquid and solid, the diflfijse ring and diffraction spots were both present, but each was of

diminshed intensity.

5.4.2 Spatial Resolution Experiment

The temperature of the heater on the gallium test cell was adjusted to maintain a stationary

position of the liquid-solid boundary. Transmission XRD images were recorded for a number of

positions of the boundary with respect to the 1 mm diameter x-ray beam, by moving the gallium

container vertically. The diffraction spot intensity was examined as a function of position of the

x-ray beam relative to the liquid-solid interface. A region of interest was defined to enclose each

diffraction spot. Spot intensity was determined as described previously.

Figure 57. Photograph of the gallium test cell.

61
XPD Sensor

Image

Radiographic

Image

boiia

Gallium

Near

Solid/Liquid

Boundry

Liquid

Gallium

Figure 58. Radiographic images and transmission XKD images with the x-ray beam probing the

solid (top), the solid/liquid boundary (middle), and the liquid (bottom). The upper

portion of the radiographic image is brighter, because the x-rays are less attenuated by

the lower-density solid gallium.

Figure 59 shows a plot of the relative intensity of the brightest diffraction spot as a fiinction of

vertical position. The position of the x-ray beam ranges from fully in the solid (0 mm) to a

position fully in the liquid (0.8 mm). The plot indicates that the XRD technique has a spatial

resolution (0.8 mm) roughly equal to the diameter of the probing x-ray beam (1 mm). The profile

plotted in Figure 59 is the convolution of the the sensed area (a small circular x-ray beam) with

the actual physical boundary. The resolution of the sensed position may be improved by

deconvolution to remove the effects caused by the finite-size of the x-ray beam.

5.4.3 Diffraction Experiments with the Energy-Sensitive Detector

Transmission diffraction experiments were also performed with the germanium (energysensitive) detector in place of the x-ray imager. The much higher efficiency of the germanium

detector, compared with the x-ray imager, required replacement of the coUimating apertures. The

1 mm diameter aperture, used in experiments with the x-ray imager, produced a diffracted beam

too intense for the detector electronics. An aperture 0.2 mm in diameter was used.

62
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Figure 59. Relative intensity of one diffraction spot as a function of the displacement as the x-ray

beam was moved with respect to the liquid-solid boundary in the gallium test cell.

Figure 60 shows transmission spectra recorded for acquisition times of 30 s. A source- specimen distance of 250 mm and a specimen-detector spacing of 180 mm was used for these

experiments. The detector collimator was not used for these experiments. The spectra were

obtained with an x-ray tube potential of 160 kV and a tube current of 1 mA. The energy spectra

below 90 keV are not shown because of the complexity introduced by the characteristic x-ray

peaks from the tungsten x-ray source and fluorescence radiation from the lead collimating

apertures on the x-ray source.

The spectral peaks at approximately 100 keV and 130 keV are produced by x-ray diffraction

spots from the solid gallium. There were no discernible peaks in the spectrum recorded with the

liquid gallium. Although the intensity was higher for the diffraction spots, the spots were highly

localized. The spectrum for the liquid specimen records more counts in each energy interval,

although the intensity is lower, because spatially it is a very large ring, which illuminates more of

the detector.

While the gallium fixture was in place, we took the opportunity to investigate the effects of

mold material when recording the diffracted energy spectrum. Figure 61 shows the measured

transmission diffraction spectrum when a piece of ceramic mold material 10 mm thick was placed on the exit side of the gallium specimen. The spectra show that the transmitted intensity is decreased by the mold, but that the spectral shape is changed very little.

63
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from molten gallium.

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Figure 61. Transmission x-ray diffraction spectrum of a single-crystal of gallium and the spectrum

when a piece of mold material 10 mm thick was placed in front of the gallium.

64
5.4.3.1 Preliminary Experiments to Study Fraction of Solid Along the X-Ray Beam Path

The effects of varying the path lengths of liquid and solid metal encountered by the probing x- ray beam were studied by constructing a dual step-wedge specimen (Fig. 62). Acrylic plastic was

machined to produce two step-wedge cavities. The cavities were filled with gallium metal. One

of the step wedges was electrically heated to melt the gallium. The other step-wedge, thermally

isolated by the acrylic plastic, remained in a solid form. With the two wedges aligned, the x-ray

path length through gallium remains the same (14 mm) for each step; however, the percentages of

liquid and solid vary. The x-ray path length through the acrylic plastic is identical for each set of

steps.

The step wedge that was to contain solid gallium was melted and then cooled slowly to

produce a single-crystal. Transmission XRD images of the solidified gallium in this step wedge

showed the same spatial position of diffraction spots for each of the steps, indicating a singlecrystal specimen had been produced.

An x-ray beam (160 kV, 1 mA) 1 mm in diameter was directed through the two wedges (one

liquid and the other solid). Figure 63 shows the arrangement of x-ray source, collimator, stepwedge, beamstop, and germanium detector. Detector shielding (not shown in the figure) was

necessary to prevent stray radiation (leakage from the tube housing and scatter from the room)

from corrupting the measured transmission spectra from the gallium wedges. Transmission

spectra (Fig. 64) were recorded (30 s live time) for each set of steps by moving the step-wedge

vertically. The broad diffraction peak at 130 keV begins to disappear as the x-ray beam probes

regions with decreasing amounts of crystalline solid. Measurement of the fraction of solid from

the diffraction spectrum appeared feasible.

step

1

% Solid

2 17

3 33

4 50

5 67

6 83

100

Figure 62. Drawing of the dual step wedge test specimen used for studies of diffraction from

differing relative path lengths through liquid and solid.

65
Figure 63. Photograph of the apparatus used for energy-sensitive transmission diffraction

experiments on a dual step-wedge gallium specimen.

11500

11000

9000

110 120 130 140

X-Ray Energy (keV)

150

Figure 64. Transmission x-ray diffraction spectra recorded during the dual gallium step-wedge

experiments.

66
5.5 Medium Temperature (<1000 °C) Furnace Experiments

Figure 65 illustrates the key elements in the apparatus used for transmission XRD

measurements during melting and solidification of aluminum and copper. The x-ray tube, with

supplemental lead shielding on the tube housing, is on the right side of the picture. The collimated

beam (1 mm in diameter) passes through the furnace (white cylinder in the center), through a quartz specimen tube, and into the metal specimen. A portion of the x-rays entering the specimen

is diffracted. The x-ray imager (black cylindrical object on the left) detects and displays the x-ray

diffraction pattern. The tungsten beam-stop is mounted between the furnace and the x-ray

imager.

5.5.1 Aluminum Melting Experiments

A melting and recrystallization experiment was performed on an aluminum specimen in the

gradient furnace. A 22 mm diameter, coarse grained polycrystalline, 99.999 percent pure

aluminum rod, in a quartz tube (2.2 mm wall thickness, 27 mm i.d.), was placed in the furnace.

Figure 66 shows the transmission Laue x-ray diffraction patterns obtained during heating, melting,

and then resolidification of the aluminum. As the rod was heated, the diffraction pattern changed,

reflecting changes in the physical state of the specimen. The complex diffraction patterns in the

first few frames of the image sequence are the result of interactions of x-rays with many crystals in

the polycrystalline specimen. As the temperature was raised further, the larger grains in the

polycrystalline rod grew at the expense of the smaller ones (Ostwald ripening), and the diffraction

Figure 65. Apparatus for observing transmission diffraction during melting and solidification of

metal.

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pattern became simpler as the x-ray beam encountered fewer, but larger, crystals. Near the

melting point (652 °C), the diffraction pattern began to lose order. The Laue pattern degenerated

into a diffiise ring of scattering when the aluminum was flilly melted. The difference between the

patterns produced by the solid aluminum and the liquid aluminum was dramatic and unmistakable.

The Laue diffraction spots disappeared at the same time the diffuse ring formed. As the aluminum

cooled below the melting point, the diffraction spots reappeared at the same time that the diffuse

ring disappeared. The diffraction pattern for the resolidified aluminum specimen was coarser,

indicating an x-ray path passing through a few, large grains, or grains favorably oriented to

diffract the intense characteristic radiation from the tungsten-target x-ray source.

In an identical heating experiment, the polycrystalline aluminum rod was heated to a temperature of only 610°C, where grain growth would occur without mehing. The specimen was

then cooled and sectioned for analysis. Figure 67 shows polished and etched cross sections of the

virgin polycrystalline rod and the annealed rod, confirming that the initial reduction in the number

of diffraction spots during the initial portion of the experiment was a result of grain growth.

Figure 67. Micrographs of polished and etched specimens from an aluminum melting experiment.

Left: polycrystalline rod, before mehing. Right: specimen after annealing.

5.5.2 Copper Melting Experiment

A polycrystalline copper rod 12.7 mm in diameter was placed in a quartz tube (2.2 mm wall

thickness), which had a triangular cross section. The tube was then inserted into our gradient

fiirnace. A collimated x-ray beam 1 mm in diameter was directed into the fiirnace, and the real- time x-ray imager was placed on the opposite side of the fiirnace to record the transmission

diffraction pattern. The x-ray technique factors were 1 60 kV and 1 mA.

The entire fijrnace could be manipulated remotely to move it vertically and horizontally. The

vertical movement was used to scan the x-ray beam and imager with respect to the liquid-solid

copper boundary that can be established in the gradient fijrnace. Horizontal movement across the

wedge-shaped copper specimen permitted interrogating different thicknesses.

69
Figure 68 shows a collage of XRD images recorded as the temperature of the furnace was

raised, to melt the copper, and then lowered, to solidify it. The sequence of warming and cooling

was repeated several times. As in the aluminum melting experiments, the solid copper produced

diffraction images with many bright Laue diffraction spots. When the melting temperature of

copper was exceeded, the ordered diffraction pattern disappeared and was replaced by a diffuse

ring of x-ray scattering from the molten copper. The diffuse scattering ring was observed in many

of the diffraction images. This was presumably the result of partial melting of the copper rod near

the outside surface of the specimen. Rapid heating was not possible because the upper

temperature limit of the furnace was close to the melting temperature of copper.

5.6 Sensing Solidification During Investment Casting

A directional solidification furnace, used for prototype single-crystal turbine blade castings,

was fitted with an x-ray source and real-time x-ray imager as shown in Figure 69. X-rays are coUimated and directed through a borosilicate glass entrance port into the vacuum furnace. The

x-ray beam passed through bats of fiberous cermaic insulation, through the molybdenum furnace

windings, through the alumina core of the hot zone of the furnace, through the casting mold, and

into the nickel-alloy specimen. Diffracted x-rays from the specimen were transmitted through the

remaining portion of the specimen and the exit wall of the mold. Attenuation along the exit path

of the diffracted x-rays through alumina, molybdenum, insulation, and borosilicate glass port

reduced the intensity of the diffraction spots. No beamstop was required because the intensity of

the primary beam was not high enough to damage the imager.

Before the casting experiments, tests were performed to determine whether diffraction from

furnace components would interfere with the patterns produced by a casting. The 10 mm thick

borosilicate glass ports were placed in our laboratory XRD apparatus (253 mm source-specimen

distance, and 381 mm source imager distance). The diffraction patterns are shown in Figure 70.

Profiles through these images are shown in Figure 71. The relatively featureless diffraction

patterns from the amorphous glass should not interfere with diffraction from a metal specimen in

the furnace. The pattern does not introduce new spots, but does reduce intensity.

The borosilicate glass ports of the directional solidification furnace attenuate both the incident

and diffracted x-rays. A single-crystal N5 casting, in its mold, was placed in the unheated

furnace. The x-ray source (320 kV and 3 mA) and x-ray imager were positioned, and specimen

rotation adjusted, to obtain three strong diffraction spots from the alloy casting. XRD images were recorded for three cases: (a) no ports on the furnace, (b) one, and then (c) both glass ports

attached to the furnace. Figure 72 shows the relative transmission of the primary beam and of one

of the diffraction spots (approximately 200 keV energy) for the three configurations of the ports.

This experiment, confirmed by modeling, revealed that a significant improvement in diffraction

spot intensity could be achieved by replacing the glass ports with a lower-attenuation material. As

discussed in section 4, replacement of the glass ports with the graphite/epoxy ports increased

signal-to-noise ratio by a factor of 1.5.

70
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71
Figure 69. Resistively heated directional solidification fijrnace, fitted with a collimated x-ray source and real-time x-ray imager for transmission x-ray diffraction studies during

casting of single-crystal nickel superalloys. The radiation shielding enclosures have

been removed to show the x-ray source (on the right) and the imager (on the left). The motion control stages can be used to move the x-ray source and imager laterally or vertically.

72
Figure 70. X-ray diffraction patterns (320 kV, 3 mA) recorded for one (left) and two (right) of

the borosilicate glass ports from the directional solidification furnace.

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Figure 71. Gray-level profiles through the XRD patterns from the borosilicate glass furnace ports.

The single broad peak in the radial distributions is characteristic of diffraction from an amorphous material.

73
Exit Poits

5 10 15

Thickness of Borosilicate Glass (mm)

20

Figure 72. Measurements of x-ray transmission through the 10 mm thick borosilicate glass ports

of the directional solidification furnace. The plots are normalized to the value of

transmission with no ports attached to the furnace. A mold-encased N5 casting (3 mm

thick) was in the fornace during all measurements.

In another laboratory test, we recordeded the x-ray diffraction pattern (320kV, 3 mA) from a hot zone identical to that in the furnace. The hot zone was constructed with molybdenum

windings on an alumina core. Figure 73 shows the diffraction patterns recorded from the hot zone (top) and the hot zone with a nickel-alloy single-crystal 6.2 mm thick inside it (bottom).

There were some x-ray diffraction spots of low-intensity from the molybdenum windings in the

contrast-enhanced image of the hot zone alone (left). The most striking feature of the image on

the left is the shadow of the molybdenum heater windings. Even though the x-ray beam was

collimated, Compton scattering from the alumina core of the hot zone produced x-rays of enough

intensity to form a radiographic image of the hot zone. Placing the nickel specimen in the hot zone severely attenuates the scatter which produced the radiographic artifacts in the left image.

The nickel specimen becomes the dominant x-ray diflfractor and produces a ring of high-intensity

diffraction spots, with minimal interference from the interactions with the hot zone.

These laboratory tests on the fiimace ports and the hot zone demonstrate that the x-ray

diffraction from a nickel specimen of moderate thickness should be observable, despite

interference from, and attenuation by, furnace components.

74
Figure 73. X-ray diffraction patterns from both the hot zone (molybdenum windings on an

alumina core) (top) and the hot zone with a nickel-alloy single-crystal in it (bottom).

Scatter from the alumina furnace core broadens the x-ray beam and forms a

radiographic-type image overlay to the diffraction pattern. The dark bands in the top

image are the result of higher attenuation in the molybdenum windings.

75
5.6.1 XRD Tests in the Directional Solidification Furnace

Before heating the furnace, we placed the 6.2 mm nickel-alloy single-crystal (on a rotational

stage) into the center of the furnace. The x-ray system was adjusted for a tube voltage of 320 kV

and a tube current of 3 mA. X-ray diffraction images were recorded as the specimen was rotated

in the collimated x-ray beam. Figure 74 shows XRD images of the specimen within the furnace,

for two different rotations of the specimen. The bright spot at the right edge of the images is the

primary x-ray beam. No beamstop was used.

Figure 74. XRD images from a nickel-alloy single crystal 6.2 mm thick placed in the directional

solidification furnace. The two images were recorded for different rotations of the

specimen.

76
An experiment was performed to identify the lattice planes responsible for particular

diffraction spots. A previously-cast, nickel-alloy single-crystal 3 mm thick in a mold (5 mm wall

thickness) was placed in the directional solidification furnace. The collimated x-ray beam (320

kV, 3 mA) 1 mm in diameter produced x-ray diffraction patterns similar to that shown in Fig. 74.

The x-ray imager was translated to place the primary x-ray beam at the center of the field of view

of the imager. The position of the translation stages was noted. Various diffraction spots were

brought into view by rotating the specimen about the vertical axis. For each spot, the translation

stages of the imager were used to position the particular diffraction spot at the center of the

imager. The position of the stages was recorded. From the two sets of translation stage positions

(primary beam and diffraction spots), we were able to determine the position of the diffraction

spot relative to the primary beam. A diffracted angle, 20, was computed for each diffraction spot

(arctangent of the spot position with respect to the primary beam divided by the 425 mm

specimen to imager distance). The energy of each diffraction spot was estimated by decreasing

the x-ray tube potential until the spot vanished. Tube current was adjusted to compensate for the

intensity changes produced as the tube potential was varied. A lattice spacing was computed

(Bragg Law) from the scattering angle and the x-ray wavelength. Table 4 contains the data and

computed parameters. The lattice spacings fall into two groups. The group clustered around

1.277 A represent reflections from the (220), (440), (660), etc. planes (lattice spacing for the 220

planes in nickel is 1.24592). The second group, clustered around 2.0853 A, are reflections from

the (111), (222), (333), etc. planes (lattice spacing for the 1 1 1 planes in nickel is 2.03458).

Table 4. Calculation of lattice parameters from XRD data.

Spot

ID

Distance (mm)

from primary

beam to spot

20

n

Tube potential

(kV) when spot

extinguishes

Wavelength (A)

when spot

extinguishes

Computed lattice spacing

X/[2 sin0] (A)

1 28.47 3.83 144 0.0861 1.288

2 22.15 2.98 180 0.0689 1.323

3 21.37 2.88 180 0.0689 1.371

4 29.84 4.02 145 0.0855 1.220

5 34.84 4.69 128 0.0969 1.185

6 37.02 4.98 112 0.1107 1.275

7 14.82 2.00 170 0.0729 2.093

8 12.15 1.64 194 0.0639 2.236

9 24.02 3.24 114 0.1088 1.927

77
5.6.2 Experiments with the Germanium Detector

The efficiency of our 13 mm thick germanium energy-sensitive detector is quite high, making

it attractive for detecting diffracted beams of high energy. As discussed in section 2, x-ray

diffraction is manifested spatially as spots, or as peaks in the transmission energy spectrum. A

diffraction spot contains one energy or energies related by integer multiples (diffraction orders).

Several experiments were performed with our germanium detector replacing the imager as an x- ray detector. A lead collimator (25 mm thick, 3.5 mm diameter hole) could be affixed to the

detector, permitting small areas of the x-ray diffraction field to be probed.

A previously cast single-crystal of N5 alloy 6 mm thick in a mold of 5 mm wall thickness was

placed in the unheated directional solidification furnace. This casting, which had a wedge shaped

cross section, permitted investigation of different thicknesses of the casting by moving our x-ray source and detector laterally. Figure 75 shows the x-ray diffraction image recorded for this

experiment. After the image was acquired, the x-ray imager was replaced by the germanium

detector. Figure 76 plots transmission spectra with the germanium detector, positioned at the

center of the primary beam or at the center of diffraction spot 4 (the one to the left of the primary

beam). The small spectral peaks in the 70 to 90 keV range are K-characteristic x-rays lines from

the lead collimators on the x-ray source and detector. The prominent spectral peak at 180 keV is produced by x-ray diffraction in the N5 specimen.

Without moving either the specimen or the x-ray source, the germanium detector was

translated laterally (to vary the angle where diffraction was measured) in increments of 2 mm

across the XRD spot. A spectrum was acquired at each position. Figure 77 shows that the peak

energy is a smooth function of the diffraction angle from the specimen. As the diffracted angle is altered, the energy required to satisfy the Bragg equation changes. The difference in the height of

the spectral peaks results from changes in the intensity of the incident x-ray spectrum at these

energies and the efficiency of transmission x-ray diffraction. Refer to our model for transmission

diffraction (section 3), which shows changes in efficiency of diffraction as a function of x-ray

energy.

5.6.3 Producing Single-Crystal Castings

The directional solidification furnace was used to produce several single-crystal test castings

before beginning the XRD experiments. A mold to produce a cylindrical casting was placed in the

furnace, and a nickel-alloy charge placed in the crucible at the top of the mold. The charge was

melted and a slow withdrawal initiated in an attempt to cast a single-crystal. After casting, the

specimen was chemically etched to disclose the crystalline structure. No crystal boundaries were

apparent. The high-energy transmission XRD system was used to evaluate the structure of the

casting. The diffraction pattern from the cylinder (Fig. 78) clearly indicates that it is a singlecrystal.

78
\Figure 75. Transmission XRD image (320 kV, 0.75 mA) of a mold-encased N5 specimen

placed in the directional solidification furnace. The bright area at the upper right is the primary x-ray beam. There are three XRD spots, to the left and below the

primary beam.

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Figure 76. Transmission spectra with the collimated germanium detector positioned at the center

of the primary beam or at the center of diffraction spot 4.

79
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Figure 77. Transmission spectra recorded as the collimated germanium detector was translated

laterally across the diffraction spot to the left of the primary, in increments of 2 mm.

I

Figure 78. Transmission x-ray diffraction pattern (320 kV, 3 mA) obtained through the center of

the cylindrical nickel-alloy specimen (15.6 mm in diameter) which was cast in the

directional solidification ftirnace.

80
5.6.4 XRD During Investment Casting

A charge of N5 nickel-alloy was placed in the crucible at the top of the flat bar mold (3 mm

thick by 38 mm wide cavity), the mold placed on the ram of the furnace, and the procedures listed

in Table 5 followed to cast a single-crystal specimen.

Table 5. Procedures for operating the directional solidification fljrnace.

Step Procedure

1 Open the gate valve between the load chamber and the furnace and use the

roughing and diffusion pumps to produce a 1 Pa vacuum

2 Close the gate valve to the load chamber, bring the chamber to atmospheric

pressure

3 Load the alloy charge into the crucible at the top of the mold and place the

mold on the vertical ram

4 Close the gate valve, rough pump the load chamber to 3 Pa, and then open

the gate valve

5 Ramp (over 30 min) both the upper and lower portions of the hot zone to a temperature of 260 °C (500 T)

6 Ramp (over 30 min) both the upper and lower portions of the hot zone to a temperature of 538 °C (1000 °F)

7 Ramp (over 30 min) both the upper and lower portions of the hot zone to a temperature of 1093 T (2000 °F)

8 Slowly raise (over 30 min) the mold into the hot zone, pausing if the vacuum

deteriorates due to outgassing from the mold

9 Dwell for 45 min

10 Rapidly ramp (over 10 min) both the upper and lower portions of the hot zone to a temperature of 1566 °C (2850 °F)

11 Dwell for 30 min

12 Withdraw the casting from the hot zone, at a rate of 150 mm/h (6 in/h).

81
By removing the collimator of the x-ray source, we could form a radiographic image of the

mold, with an approximately 30 mm field of view. Figure 79 (left) shows the grain selector of the

bar mold before any N5 had melted. Figure 79 (right) shows a radiographic image of the grain

selector immediately after it had been filled with molten N5 alloy. We radiographically observed

filling of the bar mold with molten N5 material. After all the N5 had melted, the fiimace ram was

used to slowly withdraw the mold through the temperature gradient established between the hot zone and the cold plate in the fiirnace.

The collimator was placed on the x-ray tube, and the x-ray source and x-ray imager were

scanned in unison over the mold in an attempt to observe x-ray diffraction spots fi^om the

solidifying N5 alloy. The x-ray techniques factors were 320 kV and 3 mA. No diffraction spots

from the solid were found. Apparently, the solidification front was much lower than expected,

and was below our field of view. The withdrawal of the mold from the fiarnace was completed,

and the N5 was allowed to cool.

A second N5 casting experiment was performed. This time the mold with the wedge-shaped

cross section was used. We thought that a greater thickness of N5 would lead to more intense

(and hence more easily observable) diffraction spots.

The collimated x-ray source and imager were scanned to the thin edge of the wedge and then

across it to thicker parts of the wedge. No diffraction spots were apparent. We suspected that

the solidification of the N5 was again occurring below our field of view. The x-ray beam was

positioned toward the thin edge of the wedge, the hot zone of the fijrnace was turned off", and we

observed the x-ray diffraction pattern as the N5 began to cool and solidify. A diffraction spot

began to appear in the center of the image, just above the primary x-ray beam.

At this point modifications were made to the fiarnace to raise (with an alumina foam spacer)

the location where solidification occurred into the field of view of the XRD system. We also

replaced the glass furnace ports with graphite-epoxy ports and changed the scintillator on the x- ray imager. The details of the changes made to the furnace, and to the x-ray imager were detailed

in section 4 of this report. The brightness of the XRD spots increased by approximately an order

of magnitude when the ports and scintillator were changed.

In the next experiments, the x-ray beam was directed into the base of the starter block of the

casting just above the water-cooled ram of the directional solidification furnace. Solidification of

elongated polycrystals was expected in this region. Several weak XRD spots were observed.

Rotation of the casting brought the spots into and out of view of the x-ray imager. We used the

motion stages on the x-ray source and imager to scan vertically into the fiannel-shaped region of

the mold. Initially, when this area was liquid, no diffraction spots were observed. As the

solidification progressed upward, the flinnel-shaped area began to solidify and diffraction spots

began to form. Transmission XRD spots were observable when the x-ray beam was directed into a solidified region of the casting. Generally, only one diffraction spot was observed at a time,

ahhough others could be brought into the small field-of-view of the x-ray imager, by rotating the

casting.

82

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83
We optimized (by rotating the specimen) the intensity of a particular diffraction spot and used

the motion stages on the x-ray source and imager to scan the probing x-ray beam vertically. The

diffraction spot intensity was highest in the lower (solid) portion of the casting and gradually

decreased in intensity as the XRD sensor probed regions higher (more liquid) in the casting.

Repeated vertical scans, both up and down (Figure 80), showed the same behavior in intensity

increase (more solid) and decrease (more liquid) in the diffraction spot. Other diffraction spots were rotated into view and additional vertical scans performed. The intensity of these diffraction

spots varied in the same manner.

5.6.3.1 Probing the Dendritic Region of Solidification

Bar molds were fabricated with holes for thermocouples. This permitted us to measure the

vertical temperature profile in the casting. The plan was to acquire temperature information so

that our XRD data could be quantitatively compared with predictions of the fraction of solid versus temperature. Figure 81 is a drawing of the mold, with dimensions and thermocouple

locations shown. Type C thermocouples were used. A small amount of alumina cement was used

to affix the bead of the thermocouple in the hole through the mold. Additional cement was

applied to seal the hole. The length of the thermocouple wires was trimmed so they reached

about 50 mm below the base of the mold. This location was below the top of the water-cooled

ram of the furnace, and so never reached high temperature.

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Vertical Position (mm)

75 80

Figure 80. Intensity of an intense diffraction spot plotted as a function of vertical position in the

casting. The x-ray source and imager were scanned upward from a solid region ofN5

into areas containing less solid and more liquid and then scanned down the casting.

84
Casting Mold

d

X

in

OQ

Thermocouple

Positions

15cfn

,^ Grain

Selector

Starter Block

Figure 81. Drawing of the mold, which had provisions for placement of thermocouples. Holes were left in the mold so four thermocouples could be inserted and cemented in place.

In several of the casting experiments, a woven ceramic sheathing was used to cover the bare

thermocouple wire. This sheathing was replaced with alumina tubes in later experiments.

Extension wire was welded to the thermocouples and connected to an insulated

feedthrough on the load chamber of the furnace. The extension wires were slightly coiled to

prevent kinking as the mold (with attached thermocouples) was raised into the hot zone of the

furnace. Software, written for a computer-based acquisition board, was used to periodically read

the temperature of the thermocouples and write the data to a file.

The molds were fabricated from a refractory oxide mixture to produce bar-shaped castings 6

mm thick and 25 mm wide. A 350 gram charge of N5 was placed in the crucible at the top of the

mold, and the mold placed on the furnace ram. The procedures given in Table 5 were followed.

A few minutes after the end of the the final temperature ramp to 1566 °C, droplets of molten N5

were observed, filling the starter block in the mold. The remainder of the mold filled with N5 a few minutes later. After allowing the temperature of the mold and alloy to stabilize at for 30 min,

the mold was slowly withdrawn from the hot zone at a rate of 150 mm/h. Solidification began at the base of the starter block, which rests on the water-cooled ram, and proceeded upward into the

grain selector as the mold was withdrawn from the furnace. The structure of the casting from the

grain selector upward was that of a single crystal. Polished and etched sections of the completed

casting showed a dendritic structure with several phases and an absence of grain boundaries.

85
The thermocouple temperature data were well behaved (Figure 82) until the end of the last temperature ramp to 1566 °C. At this temperature, the data became extremely noisy. The

electrical power to the hot zone of the furnace was turned off, to determine if noise pickup from

the heating element power supplies caused problems in the thermocouple readings. The effect of

turning off the furnace power was minimal. During several experiments, output from one or more

thermocouples was lost. Noise on the remaining thermocouples remained high. The erroneous

readings from thermocouples and the noise in all readings precluded using the temperature data as planned. We tried to remedy the temperature measurement difficulties, but did not succeed.

Filling of the mold was observed radiographically by removing the collimator (lead apertures)

from our x-ray source. A field of view 3 1 mm in diameter could be observed in the casting with our 50 mm diameter x-ray imager. X-ray technique factors of 180 kV, 1 mA (1.2 mm diameter

focal spot) produced acceptable images of the casting within the hot zone of the furnace.

The x-ray beam and imager were then lowered (using the remotely controlled motion stages) to the alumina foam spacer beneath the hot zone. The foam provides a low-loss path for x-rays

and a clear field of view for the XRD solidification experiments. We waited until the casting had

withdrawn to the point where the x-ray beam was centered in the funnel-shaped area of the

casting, just above the grain selector. The collimator was placed on the x-ray source to configure

the system to observe x-ray diffraction, and the tube potential and current raised to 320 kV and 3

mA. The higher tube voltage and current were necessary to produce x-rays able to penetrate

through both the mold and the alloy casting.

2000

O 1500

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(0

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1000 2000 3000 4000 5000 6000 7000

Time (sec)

Figure 82. Temperatures in the casting measured during directional solidification.

86
The casting was manually rotated, by turning the ram, while observing the real-time

transmission x-ray image. Before the solidification fi-ont advanced to the region probed by the x- ray beam, only the primary beam was visible. Eventually, solidification proceeded into the area probed by the x-ray beam and diffraction spots appeared. Rotating the specimen caused the spots

to appear, move along hyperbolic paths through the center of the primary beam, and then

disappear. The spots were produced as different lattice planes in the single-crystal casting

satisfied the conditions for Bragg reflection. Since we were using a white beam source, there was

not a singular angle where a spot appeared, but rather there was a small range of specimen

orientations over which a spot was produced. The highest intensity spot was obtained when the

peak intensity in the bremstrahlung spectrum from the x-ray source had the correct wavelength

for the particular Bragg reflection.

The single-crystal structure in a casting could be confirmed by spatially scanning the x-ray source and imager. If the diffraction pattern remained the same, the region scanned possessed a singlecrystal structure. After confirming crystal structure of a solidified portion of the casting, the x-ray source and imager were scanned vertically from the crystalline (solid) region through the region of

dendritic solidification into a fially mohen region of the casting. During the scan the XRD spot

intensity decreased, as shown in Fig. 80. During similar tests, we acquired an extensive set of data.

The raw intensity data must be processed to account for the physics of the diffraction

interaction and the spatial smoothing produced by an x-ray beam of finite-size scanned past a moving solidification front. As the x-rays pass through the region of dendritic solidification, their

path is partially solid and partially liquid. Interaction of the x-rays with the crystalline solid

produces diffraction spots. Interactions with the liquid does not contribute to spot intensity.

Rather, it attenuates the incident x-ray beam and the beam diffracted from the solid, and

contributes to a diffuse diffraction ring. As described in section 3, the spot intensity varies linearly

with the fraction of solid. A model (Lever) prediction of the fraction of solid versus temperature for N5 alloy is plotted

in Figure 83 along with the measured gray level of the transmission diffraction spot. Since the

temperature profile in the casting was not measurable in this experiment, we have adjusted the

vertical and horizontal scale of the XRD data to coincide with the solidification model predictions.

It is encouraging that the shape of the modeled and experimental curves are similar. The

experimental data also appear to show formation of the predicted second phase (break in the

curve).

5.6.3.2 X-Ray Topography of Dendrites During Solidification

In one of the casting experiments, the single crystal [001] axis was exactly aligned with the

vertical axis of the fijrnace ram. With the x-ray beam slightly angled with respect to the (001)

planes, a strong Bragg refiection was observed directly above the primary beam. The spot

remained, but its mottled appearance changed as the specimen was rotated about a vertical axis.

87
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0)

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0.4

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1200 1300 1400

Temperature (deg-C)

1500

Figure 83. Gray level of the transmission XRD spot plotted along with model (Lever) predictions

of the fraction of solid versus temperature for N5 alloy.

We think that this area (Fig. 84) of the XRD image is a transmission topograph of dendrites in the solidifying casting. Bright areas in the spot represent reflections from crystalline solid with a

[001] orientation. Dark areas are either molten alloy or misaligned areas of the solid. A topograph is a specular reflection from crystalline planes. Figure 85 shows the geometry of

topography. Reflections occur from lattice planes in correctly aligned dendrites. There are no

reflections from the amorphous liquid surrounding the dendrites. As can be seen from the figure,

there is a vertical exaggeration of the actual structure in the topograph. Additionally, there is a

vertical enlargement due to divergence of the coUimated x-ray beam. For the geometry of this

experiment, this vertical magnification is estimated to be 1.8 (divergence of 1.6 x l.l topographic

magnification). The horizontal enlargement of structure in the topograph is caused solely by

divergence of the x-ray beam, so horizontal magnification for this experiment is approximately

1.6.

Scans in the casting showed that the XRD spot intensity changed, as before, with vertical

position in the casting. The topograph became less mottled and more solid when the x-ray beam

was directed into the solidified crystal and had a more threadlike appearance higher in the casting

where there was more molten alloy and less solid. The XRD spots, including the topograph,

disappeared when the x-ray beam passed through only molten N5. The 001 topograph was best

displayed during specimen rotations, where the three-dimensional character of the topograph

could be appreciated.

88
Figure 84. Transmission topograph (top center) of dendrites in an N5 casting which are aligned

with the [001] direction. The scale can be inferred by comparison with the diameter of

the primary beam (large bright area, whose actual size at the specimen is 3.5 mm).

There is an additional vertical exaggeration (1.1) caused by the topographic geometry.

The dendrites appear to be approximately 1 to 2.5 mm wide.

Figure 85. Geometry of transmission topography. X-rays reflected from lattice planes form an image of structure within the casting which have a particular crystalline orientation.

89
6. CONCLUSIONS

1

.

Transmission x-ray diffraction can serve as a noncontact sensor for locating the liquid-solid

boundary while a casting solidifies. Position, velocity, and the shape of the solidification front

may be determined.

2. High-contrast transmission diffraction patterns were observable for a single-crystal, nickelalloy specimen 6 mm thick, surrounded by mold walls 12 mm thick, during casting in a

directional solidification fijrnace.

3. Grain growth in a heated polycrystalline specimen could be monitored by observing changes in

the diffraction pattern from a complex array of small diffraction spots to a simple circular

pattern containing only a few, high-intensity spots.

4. Defects in crystal growth (bicrystal or changes in crystalline orientation) were conspicuous

during casting as changes in the transmission diffraction pattern.

5. The intensity of a diffraction spot was directly related to the solid fraction in the mushy zone

of an alloy casting.

6. Precise alignment of the beam and detector to the crystal orientation permits topographic

imaging of individual dendrites in the solidfying front.

7. PATENT

NIST filed a patent application for the x-ray diffraction solidification sensing technique on

behalf of the Consortium on the Casting of Aerospace Alloys on 24 March 1995. A patent search

had disclosed no other x-ray technique for monitoring metal solidification within a mold. The

claims made in the application include: (1) A method for monitoring an interface between

crystalline and amorphous phases of a material within a container (mold) by using the differences

in x-ray diffraction patterns of the two material forms. (2) Using the XRD sensor to define the

regions occupied by the crystalline and amorphous phases. (3) Using the XRD sensor to determine the degree of crystallization. (4) Using the XRD sensor to determine the rate of

crystallization. (5) Using the XRD sensor in a closed-loop control system for producing castings

with high yield by controlling the temperature and/or withdrawal rate of the fiirnace. (6) Using

the XRD sensor to measure the shape of the solidifying front by employing computed

tomography. (7) A diffraction sensor using gamma rays or neutrons as the radiation source.

The x-ray diffraction solidification sensor was awarded Patent # 5,589,690; Issued 12/31/96;

"Apparatus and Method for Monitoring Casting Process"; Inventors: Thomas A. Siewert,

William P. Dube, and Dale W. Fitting. A copy of the patent is included as an appendix to this

report.

90
The authors are grateful to Steve Seltzer at NIST-Gaithersburg for providing a copy of the

XCOM software. They also appreciate the financial support of this measurement technology

development project from the NIST Office of Intelligent Processing of Materials and technical

interactions with the other members of the NIST Aerospace Casting Consortium.

8. REFERENCES

[1] J.B. Walter and K.L. Telschow, "Laser ultrasonic detection of the solid front during

casting," Review ofProgress in Quantitative Nondestructive Evaluation, D.O. Thompson

and D.E. Chimenti (eds.), Vol. 15 A, 607-613, Plenum Press, New York, 1996

[2] Y. Tsukahara, C.K. Jen, and C. Neron, "Monitoring the liquid/solid interface with plate waves in the strip casting of metal plates," Review ofProgress in Quantitative

Nondestructive Evaluation, D.O. Thompson and D.E. Chimenti (eds.), Vol. 13B, 2245-

2252, Plenum Press, New York, 1994

[3] D.T. Queheillalt, Y. Lou, and H.N.G. Wadley, "Ultrasonic sensing of the location and shape

of a solid/liquid interface for crystal growth control," Review ofProgress in Quantitative

Nondestructive Evaluation, D.O. Thompson and D.E. Chimenti (eds.). Vol. 13B, 2253-

2260, Plenum Press, New York, 1994

[4] S. Goldspiel, "Radiographic control of castings," Nondestructive Testing Handbook (2nd

edition) on Radiography and Radiation Testing, L.E. Bryant and P. Mclntyre (eds.),

Section 10, 458-490, 1985

[5] R.H. Bossi, J.L. Cline, and G.E. Georgeson, "X-ray computed tomographic inspection of

castings," Review ofProgress in Quantitative Nondestructive Evaluation, D.O. Thompson

and D.E. Chimenti (eds.). Vol. lOB, 1783-1790, Plenum Press, New York, 1991

[6] J.R. Helliwell, S. Harrop, J. Habash, B.G. Magadan, N.M. Allinnson, D. Gomez, M.

Helliwell, Z. Derowenda, and D.W.J. Cruickshank, "Instrumentation for Laue diffraction,"

Rev. Sci. Instrum., Vol. 60, No. 7, 1531-1536 (1989)

[7] I.J. Clifton, M. Elder, and J. Hajdu, "Experimental strategies in Laue Crystallography," J. Appl Crystallogr., Vol. 24, 267-277 (1991)

[8] R.E. Green, Jr., "An electro-optical x-ray diffraction system for grain boundary migration

measurements at temperature," Advances in X-Ray Analysis, Plenum Press (New York),

Vol. 15, (1972)

[9] S.E. Doyle, A.R. Gerson, K.J. Roberts, and J.N. Sherwood, "Probing the structure of solids

in a liquid environment: a recent in-situ crystallization experiment using high energy

wavelength scanning," J. Cryst. Growth, Vol. 112, 302-307 (1991)

91
[10] N.R. Joshi and R.E. Green, Jr., "Continuous x-ray diffraction measurement of lattice

rotation during tensile deformation of aluminum crystals," J. Mater. ScL, Vol. 15, 729-738

(1980)

[11] O. Babushkin, R. Harrysson, T. Linback, and R. Tegman, "A high-temperature graphite

fiirnace for x-ray powder diffraction," Mea5. Sci. Tech., Vol. 4, 816-819 (1993)

[12] K.G. Abdulvakhidov and M.F. Kupriyanov, "High-temperature unit for x-ray diffraction

studies of single crystals," Imtr. Exper. Tech., Vol. 35, No. 5, 942-943 (1992)

[13] H.L. Bhat, S.M. Clark, A. Elkorashy, and K.J. Roberts, "A furnace for in-situ synchrotron

Laue diffraction and its application to studies of solid-state phase transformations," J. Appl.

Crystallogr., Vol 23, 545-549 (1990)

[14] S. Hosokawa, S. Yamada, and K. Tamura, "X-ray diffraction measurements for expanded

liquid alkali halides at very high temperature," J. Non-Cryst. Sohds, Vol. 15, 40-43 (1992)

[15] R.E. Green, Jr., "Applications of flash x-ray diffraction systems to materials testing," Proc.

Flash Rad. Symp., ASNTFall Conf. , 151-164 (1977)

[16] H.J. Kopinek, H.H. Otten, and H.J. Bunge, "On-line measuring of technological data of cold

and hot rolled steel strips by a fixed angle texture analyer," Proc. 3rd Int. Symp. on

Nondestructive Materials Characterization, 750-762 (1989)

[17] C.J. Bechtoldt, R.C. Placious, W.J. Boettinger, M. Kuriyama, "X-ray residual stress mapping in industrial materials by energy-dispersive diflfractometry," Advances in X-Ray

Analysis, Plenum Press, New York, Vol. 25, 329-338 (1982)

[18] B .E. Warren, X-Ray Diffraction, 3 8 1 pp, Dover, New York ( 1 990)

[19] L.H. Schwartz and J.B. Cohen, Diffraction from Materials, 2nd ed., Springer-Verlag,

Berlin (1987)

[20] B.D Cullity, Elemetits ofX-Ray Diffraction, 2nd ed., p 555, Addison Wesley (1978)

[21] J.H. Hubbell, H.M. Gerstenberg, and E.B. Saloman, Bibliography ofPhoton Total Cross

Section (Attenuation Coefficient) Measurements 10 eV to 13.5 GeV, Nat. Bur. Stand. (U.S.)

Internal Report NBSIR 86-3461 (1986).

[22] M.J. Berger and J.H. Hubbell, XCOM: Photon cross-sections on a personal computer, Nat.

Bur. Stand. (U.S.) Internal Report (NBSIR) 87-3567 (1987). The XCOM software

package, written for a personal computer, provides photon cross sections and attenuation

coefficients, as a function of photon energy.

[23] L.A. Azaroff, Elements ofX-Ray C?ystallography, Tech Books, Fairfax, VA, p 105 (1968)

92
[24] B.D. Cullity, ibid, pp 156-158

[25] C. T. Chantler, "Theoretical Form Factor, Attenuation, and Scattering Tabulation for Z

1-92 from E = 1-10 eV to E = 0.4-1.0 MeV," J. Phys. Chem. Ref. Data, Vol. 24, 71

(1995)

[26] D. Waasmaier and A. Kirfel, New analytical scattering factor functions for free atoms

and \on5,Acta Crystallogr. A, Vol. 151, No. 3, 416-430 (1995)

9. BIBLIOGRAPHY

The list below contains publications which describe the high-energy transmission technique for

monitoring solidification of single-crystal turbine-blade castings.

1. T.A. Siewert, W.P. Dube, and D.W. Fitting, US Patent 5,589,690, "Apparatus and method

for monitoring casting process," issued December 3 1, 1996

2. D.W. Fitting, W.P. Dube, and T.A. Siewert, "High energy x-ray diffraction technique for

monitoring solidification of single crystal castings," Proc. Eighth Int. Symp. on

Nondestructive Materials Characterization, Plenum Press, New York, (1998)

3. D.W. Fitting, W.P. Dube, and T.A. Siewert, "Real-time monitoring of turbine blade

solidification using x-ray diffraction techniques," Semi-Annual and Annual Reports of the

NIST Consortium on Casting ofAerospace Alloys, (1994-1998) (available to Consortuium

members)

4. W.P. Dube, D.W. Fitting, and T.A. Siewert, "Real-Time Sensing of the Liquid-Solid Interface

of Castings Using Transmission XRD: Experiments and an Analytical Model," Denver X-Ray

Conf, 5-8 August 1996 (Denver, CO)

5. T.A. Siewert, D.W. Fitting, and W.P. Dube, "Solidification sensing using high-energy x-ray

diffiaction,'' AdvancedMaterials and Processes, Vol. 150, No. 1, (1996)

6. D.W. Fitting, W.P. Dube, T.A. Siewert, and J. Paran, "A process sensor for locating the

liquid-solid boundary through the mold of a casting," Proc. Review ofProgress in

Quantitative nondestructive Evaluation, Plenum Press, New York, (1995)

7. D.W. Fitting, W.P. Dube, and T.A. Siewert, "Real-time sensing of metal solidification using

transmission x-ray diffraction," submitted to Research in Nondestructive Evaluation (1997)

93
10. APPENDICES

10.1 Tables of X-Ray Attenuation Coefficients as a Function of Energy

Partial and total mass attenuation coefficients (cmVg) were computed with the XCOM

software [22]. Data were computed for energies in the 20 to 500 keV range. These are the data

we used in the transmission x-ray diffraction modeling.

The partial interaction coefficients are tabulated for the coherent, Compton, and photoelectric

processes. The total attenuation coefficients are given with and without the contribution of the

coherent process.

94
Aluminum

Constituents (Atomic Number:Fraction by Weight)

13:1.00000

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02

3.000E-02

4.000E-02

5.000E-02

6.000E-02

7.000E-02

8.000E-02

9.000E-02

l.OOOE-01

l.lOOE-01

1.200E-01

1.300E-01

1.400E-01

1.500E-01

1.600E-01

1.700E-01

1.800E-01

1.900E-01

2.000E-01

2.100E-01

2.200E-01

2.300E-01

2.400E-01

2.500E-01

2.600E-01

2.700E-01

2.800E-01

2.900E-01

3.000E-01

3.100E-01

3.200E-01

3.300E-01

3.400E-01

3.500E-01

3.600E-01

3.700E-01

2.05E-01

l.lOE-01

6.86E-02

4.68E-02

3.39E-02

2.56E-02

2.00E-02

1.61E-02

1.32E-02

l.llE-02

9.38E-03

8.06E-03

6.99E-03

6.12E-03

5.41E-03

4.81E-03

4.30E-03

3.87E-03

3.50E-03

3.19E-03

2.91E-03

2.67E-03

2.45E-03

2.26E-03

2.09E-03

1.94E-03

1.81E-03

1.69E-03

1.58E-03

1.48E-03

1.39E-03

1.31E-03

1.23E-03

1.16E-03

l.lOE-03

1.04E-03

1.37E-01

1.46E-01

1.49E-01

1.50E-01

1.48E-01

1.46E-01

1.44E-01

1.41E-01

1.39E-01

1.36E-01

1.34E-01

1.31E-01

1.29E-01

1.27E-01

1.25E-01

1.23E-01

1.21E-01

1.19E-01

1.17E-01

1.15E-01

1.13E-01

1.12E-01

l.lOE-01

1.09E-01

1.07E-01

1.06E-01

1.05E-01

1.03E-01

1.02E-01

l.OlE-01

9.97E-02

9.86E-02

9.75E-02

9.64E-02

9.54E-02

9.44E-02

3.10E+00

8.72E-01

3.50E-01

1.72E-01

9.56E-02

5.82E-02

3.78E-02

2.59E-02

1.84E-02

1.35E-02

1.02E-02

7.90E-03

6.23E-03

4.99E-03

4.06E-03

3.35E-03

2.79E-03

2.35E-03

2.00E-03

1.72E-03

1.49E-03

1.29E-03

1.13E-03

9.99E-04

8.86E-04

7.90E-04

7.07E-04

6.36E-04

5.74E-04

5.21E-04

4.74E-04

4.33E-04

3.96E-04

3.64E-04

3.35E-04

3.10E-04

3.44E+00

1.13E+00

5.68E-01

3.68E-01

2.78E-01

2.30E-01

2.02E-01

1.83E-01

1.70E-01

1.61E-01

1.53E-01

1.47E-01

1.42E-01

1.38E-01

1.34E-01

1.31E-01

1.28E-01

1.25E-01

1.22E-01

1.20E-01

1.18E-01

1.16E-01

1.14E-01

1.12E-01

l.lOE-01

1.09E-01

1.07E-01

1.06E-01

1.04E-01

1.03E-01

1.02E-01

l.OOE-01

9.91E-02

9.80E-02

9.69E-02

9.58E-02

3.24E+00

1.02E+00

5.00E-01

3.21E-01

2.44E-01

2.04E-01

1.82E-01

1.67E-01

1.57E-01

1.50E-01

1.44E-01

1.39E-01

1.35E-01

1.32E-01

1.29E-01

1.26E-01

1.23E-01

1.21E-01

1.19E-01

1.17E-01

1.15E-01

1.13E-01

l.llE-01

l.lOE-01

1.08E-01

1.07E-01

1.05E-01

1.04E-01

1.03E-01

l.OlE-01

l.OOE-01

9.90E-02

9.79E-02

9.68E-02

9.58E-02

9.47E-02

95
linum

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.800E-01 9.89E-04 9.35E-02 2.87E-04 9.47E-02 9.38E-02

3.900E-01 9.40E-04 9.25E-02 2.66E-04 9.37E-02 9.28E-02

4.000E-01 8.93E-04 9.16E-02 2.48E-04 9.28E-02 9.19E-02

4.100E-01 8.51E-04 9.07E-02 2.31E-04 9.18E-02 9.10E-02

4.200E-01 8.11E-04 8.99E-02 2.16E-04 9.09E-02 9.01E-02

4.300E-01 7.74E-04 8.90E-02 2.02E-04 9.00E-02 8.92E-02

4.400E-01 7.39E-04 8.82E-02 1.90E-04 8.92E-02 8.84E-02

4.500E-01 7.07E-04 8.74E-02 1.79E-04 8.83E-02 8.76E-02

4.600E-01 6.77E-04 8.67E-02 1.68E-04 8.75E-02 8.68E-02

4.700E-01 6.48E-04 8.59E-02 1.59E-04 8.67E-02 8.61E-02

4.800E-01 6.22E-04 8.52E-02 1.50E-04 8.59E-02 8.53E-02

4.900E-01 5.97E-04 8.44E-02 1.42E-04 8.52E-02 8.46E-02

5.000E-01 5.73E-04 8.37E-02 1.34E-04 8.45E-02 8.39E-02

96
Aluminum Oxide

Constituents (Atomic Number:Fraction by Weight)

8:0.47075 13:0.52925

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02 1.55E-01 1.45E-01 1.93E+00 2.23E+00 2.07E+00

3.000E-02 8.27E-02 1.53E-01 5.39E-01 7.75E-01 6.92E-01

4.000E-02 5.14E-02 1.56E-01 2.16E-01 4.23E-01 3.71E-01

5.000E-02 3.50E-02 1.55E-01 1.05E-01 2.95E-01 2.60E-01

6.000E-02 2.53E-02 1.53E-01 5.85E-02 2.37E-01 2.12E-01

7.000E-02 1.91E-02 1.51E-01 3.56E-02 2.05E-01 1.86E-01

8.000E-02 1.49E-02 1.48E-01 2.31E-02 1.86E-01 1.71E-01

9.000E-02 1.20E-02 1.45E-01 1.58E-02 1.73E-01 1.61E-01

l.OOOE-01 9.82E-03 1.42E-01 1.12E-02 1.63E-01 1.53E-01

l.lOOE-01 8.20E-03 1.39E-01 8.23E-03 1.56E-01 1.48E-01

1.200E-01 6.95E-03 1.37E-01 6.21E-03 1.50E-01 1.43E-01

1.300E-01 5.96E-03 1,34E-01 4.80E-03 1.45E-01 1.39E-01

1.400E-01 5.17E-03 1.32E-01 3.78E-03 1.41E-01 1.36E-01

1.500E-01 4.53E-03 1.29E-01 3.03E-03 1.37E-01 1.32E-01

1.600E-01 4.00E-03 1.27E-01 2.46E-03 1.34E-01 1.30E-01

1.700E-01 3.55E-03 1.25E-01 2.03E-03 1.31E-01 1.27E-01

1.800E-01 3.18E-03 1.23E-01 1.69E-03 1.28E-01 1.25E-01

1.900E-01 2.86E-03 1.21E-01 1.43E-03 1.25E-01 1.22E-01

2.000E-01 2.59E-03 1.19E-01 1.21E-03 1.23E-01 1.20E-01

2.100E-01 2.35E-03 1.17E-01 1.04E-03 1.21E-01 1.18E-01

2.200E-01 2.15E-03 1.16E-01 8.99E-04 1.19E-01 1.17E-01

2.300E-01 1.97E-03 1.14E-01 7.83E-04 1.17E-01 1.15E-01

2.400E-01 1.81E-03 1.12E-01 6.86E-04 1.15E-01 1.13E-01

2.500E-01 1.67E-03 l.llE-01 6.05E-04 1.13E-01 l.llE-01

2.600E-01 1.54E-03 1.09E-01 5.36E-04 l.llE-01 l.lOE-01

2.700E-01 1.43E-03 1.08E-01 4.78E-04 l.lOE-01 1.08E-01

2.800E-01 1.33E-03 1.07E-01 4.28E-04 1.08E-01 1.07E-01

2.900E-01 1.24E-03 1.05E-01 3.84E-04 1.07E-01 1.06E-01

3.000E-01 1.16E-03 1.04E-01 3.47E-04 1.06E-01 1.04E-01

3.100E-01 1.09E-03 1.03E-01 3.15E-04 1.04E-01 1.03E-01

3.200E-01 1.02E-03 1.02E-01 2.86E-04 1.03E-01 1.02E-01

3.300E-01 9.64E-04 l.OOE-01 2.61E-04 1.02E-01 l.OlE-01

3.400E-01 9.08E-04 9.93E-02 2.39E-04 l.OOE-01 9.96E-02

3.500E-01 8.57E-04 9.82E-02 2.20E-04 9.93E-02 9.85E-02

3.600E-01 8.11E-04 9.72E-02 2.03E-04 9.82E-02 9.74E-02

97
Aluminum Oxide

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.700E-01 7.68E-04 9.62E-02 1.87E-04 9.71E-02 9.64E-02

3.800E-01 7.28E-04 9.52E-02 1.73E-04 9.61E-02 9.54E-02

3.900E-01 6.92E-04 9.42E-02 1.61E-04 9.51E-02 9.44E-02

4.000E-01 6.58E-04 9.33E-02 1.50E-04 9.41E-02 9.35E-02

4.100E-01 6.26E-04 9.24E-02 1.40E-04 9.32E-02 9.26E-02

4.200E-01 5.97E-04 9.15E-02 1.31E-04 9.23E-02 9.17E-02

4.300E-01 5.70E-04 9.07E-02 1.22E-04 9.14E-02 9.08E-02

4.400E-01 5.44E-04 8.99E-02 1.15E-04 9.05E-02 9.00E-02

4.500E-01 5.20E-04 8.90E-02 1.08E-04 8.97E-02 8.92E-02

4.600E-01 4.98E-04 8.83E-02 l.OlE-04 8.89E-02 8.84E-02

4.700E-01 4.77E-04 8.75E-02 9.57E-05 8.81E-02 8.76E-02

4.800E-01 4.58E-04 8.67E-02 9.04E-05 8.73E-02 8.68E-02

4.900E-01 4.39E-04 8.60E-02 8.56E-05 8.65E-02 8.61E-02

5.000E-01 4.22E-04 8.53E-02 8.11E-05 8.58E-02 8.54E-02

98
Borosilicate Glass

Constituents (Atomic Number:Fraction by Weight)

5:0.04010 8:0.53965 11:0.02820 13:0.01170 14:0.37704 19:0.00330

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02 1.52E-01 1.48E-01 2.00E+00 2.30E+00 2.14E+00

3.000E-02 8.09E-02 1.56E-01 5.61E-01 7.99E-01 7.18E-01

4.000E-02 5.04E-02 1.58E-01 2.25E-01 4.34E-01 3.84E-01

5.000E-02 3.43E-02 1.57E-01 l.llE-01 3.02E-01 2.68E-01

6.000E-02 2.48E-02 1.55E-01 6.15E-02 2.42E-01 2.17E-01

7.000E-02 1.87E-02 1.53E-01 3.75E-02 2.09E-01 1.90E-01

8.000E-02 1.46E-02 1.50E-01 2.44E-02 1.89E-01 1.74E-01

9.000E-02 1.18E-02 1.47E-01 1.66E-02 1.76E-01 1.64E-01

l.OOOE-01 9.65E-03 1.44E-01 1.18E-02 1.66E-01 1.56E-01

l.lOOE-01 8.06E-03 1.41E-01 8.71E-03 1.58E-01 1.50E-01

1.200E-01 6.83E-03 1.39E-01 6.58E-03 1.52E-01 1.45E-01

1.300E-01 5.86E-03 1.36E-01 5.09E-03 1.47E-01 1.41E-01

1.400E-01 5.08E-03 1.34E-01 4.01E-03 1.43E-01 1.38E-01

1.500E-01 4.45E-03 1.31E-01 3.21E-03 1.39E-01 1.34E-01

1.600E-01 3.93E-03 1.29E-01 2.62E-03 1.36E-01 1.32E-01

1.700E-01 3.49E-03 1.27E-01 2.16E-03 1.32E-01 1.29E-01

1.800E-01 3.12E-03 1.25E-01 1.80E-03 1.30E-01 1.27E-01

1.900E-01 2.81E-03 1.23E-01 1.52E-03 1.27E-01 1.24E-01

2.000E-01 2.54E-03 1.21E-01 1.29E-03 1.25E-01 1.22E-01

2.100E-01 2.31E-03 1.19E-01 l.llE-03 1.22E-01 1.20E-01

2.200E-01 2.11E-03 1.17E-01 9.57E-04 1.20E-01 1.18E-01

2.300E-01 1.93E-03 1.16E-01 8.33E-04 1.18E-01 1.16E-01

2.400E-01 1.78E-03 1.14E-01 7.30E-04 1.16E-01 1.15E-01

2.500E-01 1.64E-03 1.12E-01 6.44E-04 1.15E-01 1.13E-01

2.600E-01 1.52E-03 l.llE-01 5.71E-04 1.13E-01 l.llE-01

2.700E-01 1.41E-03 1.09E-01 5.09E-04 l.llE-01 l.lOE-01

2.800E-01 1.31E-03 1.08E-01 4.56E-04 l.lOE-01 1.09E-01

2.900E-01 1.22E-03 1.07E-01 4.10E-04 1.08E-01 1.07E-01

3.000E-01 1.14E-03 1.05E-01 3.70E-04 1.07E-01 1.06E-01

3.100E-01 1.07E-03 1.04E-01 3.36E-04 1.06E-01 1.05E-01

3.200E-01 l.OlE-03 1.03E-01 3.06E-04 1.04E-01 1.03E-01

3.300E-01 9.48E-04 1.02E-01 2.79E-04 1.03E-01 1.02E-01

3.400E-01 8.93E-04 l.OlE-01 2.56E-04 1.02E-01 l.OlE-01

3.500E-01 8.43E-04 9.96E-02 2.35E-04 l.OlE-01 9.98E-02

99
Borosilicate Glass> Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.600E-01 7.98E-04 9.85E-02 2.16E-04 9.95E-02 9.87E-02

3.700E-01 7.55E-04 9.75E-02 2.00E-04 9.85E-02 9.77E-02

3.800E-01 7.16E-04 9.65E-02 1.85E-04 9.74E-02 9.67E-02

3.900E-01 6.80E-04 9.55E-02 1.72E-04 9.64E-02 9.57E-02

4.000E-01 6.47E-04 9.46E-02 1.60E-04 9.54E-02 9.48E-02

4.100E-01 6.16E-04 9.37E-02 1.49E-04 9.44E-02 9.38E-02

4.200E-01 5.87E-04 9.28E-02 1.39E-04 9.35E-02 9.29E-02

4.300E-01 5.60E-04 9.19E-02 1.31E-04 9.26E-02 9.21E-02

4.400E-01 5.35E-04 9.11E-02 1.23E-04 9.17E-02 9.12E-02

4.500E-01 5.12E-04 9.03E-02 1.15E-04 9.09E-02 9.04E-02

4.600E-01 4.90E-04 8.95E-02 1.08E-04 9.01E-02 8.96E-02

4.700E-01 4.69E-04 8.87E-02 1.02E-04 8.93E-02 8.88E-02

4.800E-01 4.50E-04 8.79E-02 9.67E-05 8.85E-02 8.80E-02

4.900E-01 4.32E-04 8.72E-02 9.15E-05 8.77E-02 8.73E-02

5.000E-01 4.15E-04 8.65E-02 8.67E-05 8.70E-02 8.65E-02

100
Copper

Constituents (Atomic Number:Fraction by Weight)

29:1.00000

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02 6.06E-01 l.lOE-01 3.31E+01 3.38E+01 3.32E+01

3.000E-02 3.37E-01 1.23E-01 1.05E+01 1.09E+01 1.06E+01

4.000E-02 2.12E-01 1.29E-01 4.52E+01 4.86E+00 4.65E+00

5.000E-02 1.47E-01 1.31E-01 2.34E+00 2.61E+00 2.47E+00

6.000E-02 1.08E-01 1.31E-01 1.35E+00 1.59E+00 1.48E+00

7.000E-02 8.30E-02 1.31E-01 8.50E-01 1.06E+00 9.81E-01

8.000E-02 6.59E-02 1.29E-01 5.68E-01 7.63E-01 6.97E-01

9.000E-02 5.36E-02 1.28E-01 3.97E-01 5.78E-01 5.25E-01

l.OOOE-01 4.45E-02 1.26E-01 2.88E-01 4.58E-01 4.14E-01

l.lOOE-01 3.74E-02 1.24E-01 2.15E-01 3.77E-01 3.40E-01

1.200E-01 3.19E-02 1.23E-01 1.65E-01 3.19E-01 2.88E-01

1.300E-01 2.76E-02 1.21E-01 1.29E-01 2.77E-01 2.50E-01

1.400E-01 2.40E-02 1.19E-01 1.03E-01 2.46E-01 2.22E-01

1.500E-01 2.11E-02 1.17E-01 8.35E-02 2.22E-01 2.01E-01

1.600E-01 1.87E-02 1.15E-01 6.86E-02 2.03E-01 1.84E-01

1.700E-01 1.67E-02 1.14E-01 5.70E-02 1.87E-01 1.71E-01

1.800E-01 1.50E-02 1.12E-01 4.79E-02 1.75E-01 1.60E-01

1.900E-01 1.35E-02 l.lOE-01 4.07E-02 1.65E-01 1.51E-01

2.000E-01 1.23E-02 1.09E-01 3.49E-02 1.56E-01 1.44E-01

2.100E-01 1.12E-02 1.07E-01 3.01E-02 1.49E-01 1.37E-01

2.200E-01 1.02E-02 1.06E-01 2.62E-02 1.42E-01 1.32E-01

2.300E-01 9.39E-03 1.04E-01 2.29E-02 1.37E-01 1.27E-01

2.400E-01 8.65E-03 1.03E-01 2.02E-02 1.32E-01 1.23E-01

2.500E-01 8.00E-03 1.02E-01 1.79E-02 1.28E-01 1.20E-01

2.600E-01 7.41E-03 l.OOE-01 1.60E-02 1.24E-01 1.16E-01

2.700E-01 6.89E-03 9.93E-02 1.43E-02 1.20E-01 1.14E-01

2.800E-01 6.42E-03 9.81E-02 1.28E-02 1.17E-01 l.llE-01

2.900E-01 6.00E-03 9.69E-02 1.16E-02 1.15E-01 1.09E-01

3.000E-01 5.62E-03 9.58E-02 1.05E-02 1.12E-01 1.06E-01

3.100E-01 5.27E-03 9.47E-02 9.56E-03 l.lOE-01 1.04E-01

3.200E-01 4.96E-03 9.37E-02 8.73E-03 1.07E-01 1.02E-01

3.300E-01 4.67E-03 9.26E-02 7.99E-03 1.05E-01 l.OlE-01

3.400E-01 4.41E-03 9.17E-02 7.34E-03 1.03E-01 9.90E-02

3.500E-01 4.16E-03 9.07E-02 6.77E-03 1.02E-01 9.75E-02

3.600E-01 3.94E-03 8.97E-02 6.25E-03 9.99E-02 9.60E-02

101
Copper

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.700E-01 3.74E-03 8.88E-02 5.79E-03 9.84E-02 9.46E-02

3.800E-01 3.55E-03 8.80E-02 5.37E-03 9.69E-02 9.33E-02

3.900E-01 3.37E-03 8.71E-02 5.00E-03 9.55E-02 9.21E-02

4.000E-01 3.21E-03 8.63E-02 4.66E-03 9.41E-02 9.09E-02

4.100E-01 3.06E-03 8.54E-02 4.36E-03 9.29E-02 8.98E-02

4.200E-01 2.91E-03 8.47E-02 4.08E-03 9.16E-02 8.87E-02

4.300E-01 2.78E-03 8.39E-02 3.83E-03 9.05E-02 8.77E-02

4.400E-01 2.66E-03 8.31E-02 3.60E-03 8.94E-02 8.67E-02

4.500E-01 2.54E-03 8.24E-02 3.39E-03 8.83E-02 8.58E-02

4.600E-01 2.44E-03 8.17E-02 3.20E-03 8.73E-02 8.49E-02

4.700E-01 2.34E-03 8.10E-02 3.02E-03 8.63E-02 8.40E-02

4.800E-01 2.24E-03 8.03E-02 2.86E-03 8.54E-02 8.32E-02

4.900E-01 2.15E-03 7.96E-02 2.71E-03 8.45E-02 8.23E-02

5.000E-01 2.07E-03 7.90E-02 2.57E-03 8.36E-02 8.16E-02

102
Gadolinium Oxysulfide

Constituents (Atomic Number:Fraction by Weight)

8:0.08453 16:0.08470 64:0.83077

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon

Energy

(MeV)

2.000E-02

3.000E-02

4.000E-02

5.000E-02

6.000E-02

7.000E-02

8.000E-02

9.000E-02

l.OOOE-01

l.lOOE-01

1.200E-01

1.300E-01

1.400E-01

1.500E-01

1.600E-01

1.700E-01

1.800E-01

1.900E-01

2.000E-01

2.100E-01

2.200E-01

2.300E-01

2.400E-01

2.500E-01

2.600E-01

2.700E-01

2.800E-01

2.900E-01

3.000E-01

3.100E-01

3.200E-01

3.300E-01

3.400E-01

3.500E-01

3.600E-01

coh

(cm2/g)

1.39E+00

8.18E-01

5.33E-01

3.77E-01

2.83E-01

2.21E-01

1.77E-01

1.45E-01

1.20E-01

1.02E-01

8.73E-02

7.57E-02

6.63E-02

5.86E-02

5.22E-02

4.68E-02

4.22E-02

3.83E-02

3.49E-02

3.19E-02

2.93E-02

2.70E-02

2.49E-02

2.31E-02

2.15E-02

2.00E-02

1.87E-02

1.75E-02

1.64E-02

1.54E-02

1.45E-02

1.37E-02

1.29E-02

1.23E-02

1.16E-02

Comp

(cm2/g)

9.03E-02

1.03E-01

1.09E-01

1.12E-01

1.13E-01

1.14E-01

1.14E-01

1.13E-01

1.12E-01

l.llE-01

1.09E-01

1.08E-01

1.06E-01

1.05E-01

1.04E-01

1.02E-01

l.OlE-01

9.96E-02

9.83E-02

9.71E-02

9.59E-02

9.47E-02

9.35E-02

9.24E-02

9.13E-02

9.03E-02

8.93E-02

8.83E-02

8.73E-02

8.64E-02

8.55E-02

8.46E-02

8.37E-02

8.29E-02

8.21E-02

PE

(cm2/g)

3.54E+01

1.16E+01

5.21E+00

2.78E+00

9.42E+00

6.26E+00

4.38E+00

3.18E+00

2.38E+00

1.83E+00

1.44E+00

1.15E+00

9.38E-01

7.74E-01

6.47E-01

5.47E-01

4.66E-01

4.01E-01

3.48E-01

3.04E-01

2.67E-01

2.37E-01

2.10E-01

1.88E-01

1.69E-01

1.53E-01

1.38E-01

1.26E-01

1.15E-01

1.05E-01

9.66E-02

8.90E-02

8.22E-02

7.62E-02

7.08E-02

TOTAL

w/coh w/o coh

(cm2/g) (cm2/g)

3.69E+01

1.25E+01

5.85E+00

3.27E+00

9.81E+00

6.59E+00

4.67E+00

3.44E+00

2.61E+00

2.04E+00

1.64E+00

1.34E+00

l.UE+OO

9.38E-01

8.03E-01

6.96E-01

6.10E-01

5.39E-01

4.81E-01

4.33E-01

3.93E-01

3.58E-01

3.29E-01

3.04E-01

2.82E-01

2.63E-01

2.46E-01

2.32E-01

2.18E-01

2.07E-01

1.97E-01

1.87E-01

1.79E-01

1.71E-01

1.64E-01 1.

3.55E+01

1.17E+01

5.32E+00

2.90E+00

9.53E+00

6.37E+00

4.49E+00

3.29E+00

2.49E+00

1.94E+00

1.55E+00

1.26E+00

1.04E+00

8.80E-01

7.51E-01

6.49E-01

5.67E-01

5.01E-01

4.46E-01

4.01E-01

3.63E-01

3.31E-01

3.04E-01

2.81E-01

2.60E-01

2.43E-01

2.28E-01

2.14E-01

2.02E-01

1.91E-01

1.82E-01

1.74E-01

1.66E-01

1.59E-01

53E-01

103
Gadolinium Oxysulfide

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.700E-01 l.lOE-02 8.13E-02 6.59E-02 1.58E-01 1.47E-01

3.800E-01 1.05E-02 8.05E-02 6.15E-02 1.52E-01 1.42E-01

3.900E-01 9.97E-03 7.97E-02 5.75E-02 1.47E-01 1.37E-01

4.000E-01 9.49E-03 7.90E-02 5.39E-02 1.42E-01 1.33E-01

4.100E-01 9.05E-03 7.83E-02 5.05E-02 1.38E-01 1.29E-01

4.200E-01 8.64E-03 7.76E-02 4.75E-02 1.34E-01 1.25E-01

4.300E-01 8.26E-03 7.69E-02 4.48E-02 1.30E-01 1.22E-01

4.400E-01 7.90E-03 7.63E-02 4.22E-02 1.26E-01 1.18E-01

4.500E-01 7.57E-03 7.56E-02 3.99E-02 1.23E-01 1.16E-01

4.600E-01 7.25E-03 7.50E-02 3.78E-02 1.20E-01 1.13E-01

4.700E-01 6.96E-03 7.43E-02 3.58E-02 1.17E-01 l.lOE-01

4.800E-01 6.68E-03 7.37E-02 3.40E-02 1.14E-01 1.08E-01

4.900E-01 6.42E-03 7.31E-02 3.23E-02 1.12E-01 1.05E-01

5.000E-01 6.18E-03 7.26E-02 3.07E-02 1.09E-01 1.03E-01

104
Gallium

Constituents (Atomic Number:Fraction by Weight)

31:1.00000

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02 6.52E-01 1.05E-01 3.85E+01 3.93E+01 3.86E+01

3.000E-02 3.65E-01 1.18E-01 1.23E+01 1.28E+01 1.24E+01

4.000E-02 2.31E-01 1.24E-01 5.37E+00 5.73E+00 5.49E+00

5.000E-02 1.59E-01 1.27E-01 2.79E+00 3.08E+00 2.92E+00

6.000E-02 1.17E-01 1.27E-01 1.62E+00 1.87E+00 1.75E+00

7.000E-02 9.01E-02 1.26E-01 1.02E+00 1.24E+00 1.15E+00

8.000E-02 7.16E-02 1.25E-01 6.85E-01 8.82E-01 8.11E-01

9.000E-02 5.83E-02 1.24E-01 4.80E-01 6.62E-01 6.04E-01

l.OOOE-01 4.83E-02 1.22E-01 3.49E-01 5.20E-01 4.71E-01

l.lOOE-01 4.07E-02 1.21E-01 2.61E-01 4.23E-01 3.82E-01

1.200E-01 3.48E-02 1.19E-01 2.01E-01 3.54E-01 3.20E-01

1.300E-01 3.00E-02 1.17E-01 1.57E-01 3.05E-01 2.75E-01

1.400E-01 2.62E-02 1.15E-01 1.26E-01 2.67E-01 2.41E-01

1.500E-01 2.30E-02 1.14E-01 1.02E-01 2.39E-01 2.16E-01

1.600E-01 2.04E-02 1.12E-01 8.38E-02 2.16E-01 1.96E-01

1.700E-01 1.82E-02 l.lOE-01 6.98E-02 1.98E-01 1.80E-01

1.800E-01 1.63E-02 1.09E-01 5.87E-02 1.84E-01 1.68E-01

1.900E-01 1.48E-02 1.07E-01 4.99E-02 1.72E-01 1.57E-01

2.000E-01 1.34E-02 1.06E-01 4.28E-02 1.62E-01 1.49E-01

2.100E-01 1.22E-02 1.04E-01 3.70E-02 1.53E-01 1.41E-01

2.200E-01 1.12E-02 1.03E-01 3.22E-02 1.46E-01 1.35E-01

2.300E-01 1.03E-02 1.02E-01 2.82E-02 1.40E-01 1.30E-01

2.400E-01 9.45E-03 l.OOE-01 2.49E-02 1.35E-OI 1.25E-01

2.500E-01 8.74E-03 9.89E-02 2.21E-02 1.30E-01 1.21E-01

2.600E-01 8.10E-03 9.77E-02 1.97E-02 1.25E-01 1.17E-01

2.700E-01 7.53E-03 9.65E-02 1.76E-02 1.22E-01 1.14E-01

2.800E-01 7.02E-03 9.54E-02 1.58E-02 1.18E-01 l.llE-01

2.900E-01 6.56E-03 9.43E-02 1.43E-02 1.15E-01 1.09E-01

3.000E-01 6.15E-03 9.32E-02 1.30E-02 1.12E-0I 1.06E-01

3.100E-01 5.77E-03 9.21E-02 1.18E-02 l.lOE-01 1.04E-01

3.200E-01 5.42E-03 9.11E-02 1.08E-02 1.07E-01 1.02E-01

3.300E-01 5.11E-03 9.01E-02 9.87E-03 1.05E-01 l.OOE-01

3.400E-01 4.82E-03 8.92E-02 9.07E-03 1.03E-01 9.83E-02

3.500E-01 4.55E-03 8.82E-02 8.36E-03 l.OlE-01 9.66E-02

3.600E-01 4.31E-03 8.73E-02 7.73E-03 9.94E-02 9.51E-02

105
Gallium

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.700E-01 4.09E-03 8.65E-02 7.16E-03 9.77E-02 9.36E-02

3.800E-01 3.88E-03 8.56E-02 6.65E-03 9.61E-02 9.23E-02

3.900E-01 3.69E-03 8.48E-02 6.19E-03 9.47E-02 9.10E-02

4.000E-01 3.51E-03 8.40E-02 5.77E-03 9.32E-02 8.97E-02

4.100E-01 3.34E-03 8.32E-02 5.40E-03 9.19E-02 8.86E-02

4.200E-01 3.19E-03 8.24E-02 5.06E-03 9.07E-02 8.75E-02

4.300E-01 3.05E-03 8.17E-02 4.75E-03 8.94E-02 8.64E-02

4.400E-01 2.91E-03 8.09E-02 4.46E-03 8.83E-02 8.54E-02

4.500E-01 2.79E-03 8.02E-02 4.20E-03 8.72E-02 8.44E-02

4.600E-01 2.67E-03 7.95E-02 3.96E-03 8.62E-02 8.35E-02

4.700E-01 2.56E-03 7.88E-02 3.74E-03 8.51E-02 8.26E-02

4.800E-01 2.45E-03 7.82E-02 3.54E-03 8.42E-02 8.17E-02

4.900E-01 2.36E-03 7.75E-02 3.36E-03 8.33E-02 8.09E-02

5.000E-01 2.26E-03 7.69E-02 3.19E-03 8.24E-02 8.01E-02

106
Germanium

Constituents (Atomic Number:Fraction by Weight)

32:1.00000

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon

Energy

(MeV)

2.000E-02

3.000E-02

4.000E-02

5.000E-02

6.000E-02

7.000E-02

8.000E-02

9.000E-02

l.OOOE-01

l.lOOE-01

1.200E-01

1.300E-01

1.400E-01

1.500E-01

1.600E-01

1.700E-01

1.800E-01

1.900E-01

2.000E-01

2.100E-01

2.200E-01

2.300E-01

2.400E-01

2.500E-01

2.600E-01

2.700E-01

2.800E-01

2.900E-01

3.000E-01

3.100E-01

3.200E-01

3.300E-01

3.400E-01

3.500E-01

3.600E-01

coh

(cm2/g)

6.77E-01

3.80E-01

2.41E-01

1.66E-01

1.22E-01

9.40E-02

7.47E-02

6.08E-02

5.05E-02

4.25E-02

3.63E-02

3.14E-02

2.74E-02

2.41E-02

2.13E-02

1.90E-02

1.71E-02

1.54E-02

1.40E-02

1.28E-02

1.17E-02

1.07E-02

9.89E-03

9.14E-03

8.48E-03

7.88E-03

7.35E-03

6.87E-03

6.43E-03

6.04E-03

5.68E-03

5.35E-03

5.05E-03

4.77E-03

4.51E-03

Comp

(cm2/g)

1.03E-01

1.16E-01

1.22E-01

1.25E-01

1.25E-01

1.25E-01

1.24E-01

1.23E-01

1.21E-01

1.19E-01

1.18E-01

1.16E-01

1.14E-01

1.13E-01

l.llE-01

1.09E-01

1.08E-01

1.06E-01

1.05E-01

1.03E-01

1.02E-01

l.OlE-01

9.93E-02

9.80E-02

9.68E-02

9.56E-02

9.45E-02

9.34E-02

9.23E-02

9.13E-02

9.03E-02

8.93E-02

8.83E-02

8.74E-02

8.65E-02

PE

(cm2/g)

4.14E+01

1.34E+01

5.84E+00

3.04E+00

1.77E+00

1.12E+00

7.52E-01

5.27E-01

3.84E-01

2.87E-01

2.21E-01

1.73E-01

1.39E-01

1.12E-01

9.25E-02

7.71E-02

6.49E-02

5.52E-02

4.73E-02

4.09E-02

3.56E-02

3.12E-02

2.75E-02

2.44E-02

2.18E-02

1.95E-02

1.75E-02

1.58E-02

1.44E-02

1.31E-02

1.20E-02

l.lOE-02

l.OlE-02

9.28E-03

8.58E-03

TOTAL

w/coh w/o coh

(cm2/g) (cm2/g)

4.22E+01

1.38E+01

6.21E+00

3.34E+00

2.02E+00

1.34E+00

9.50E-01

7.10E-01

5.55E-01

4.49E-01

3.75E-01

3.21E-01

2.80E-01

2.49E-01

2.25E-01

2.05E-01

1.90E-01

1.77E-01

1.66E-01

1.57E-01

1.49E-01

1.43E-01

1.37E-01

1.32E-01

1.27E-01

1.23E-01

1.19E-01

1.16E-01

1.13E-01

l.lOE-01

1.08E-01

1.06E-01

1.03E-01

l.OlE-01

9,96E-02

4.15E+01

1.35E+01

5.97E+00

3.17E+00

1.90E+00

1.25E+00

8.75E-01

6.50E-01

5.05E-01

4.07E-01

3.39E-01

2.89E-01

2.53E-01

2.25E-01

2.03E-01

1.86E-01

1.73E-01

1.61E-01

1.52E-01

1.44E-01

1.38E-01

1.32E-01

1.27E-01

1.22E-01

1.19E-01

1.15E-01

1.12E-01

1.09E-01

1.07E-01

1.04E-01

1.02E-01

l.OOE-01

9.84E-02

9.67E-02

9.51E-02

107
Germanium

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.700E-01 4.28E-03 8.57E-02 7.95E-03 9.79E-02 9.36E-02

3.800E-01 4.06E-03 8.48E-02 7.38E-03 9.63E-02 9.22E-02

3.900E-01 3.86E-03 8.40E-02 6.87E-03 9.47E-02 9.09E-02

4.000E-01 3.67E-03 8.32E-02 6.41E-03 9.33E-02 8.96E-02

4.100E-01 3.50E-03 8.24E-02 5.99E-03 9.19E-02 8.84E-02

4.200E-01 3.34E-03 8.16E-02 5.62E-03 9.06E-02 8.73E-02

4.300E-01 3.19E-03 8.09E-02 5.27E-03 8.94E-02 8.62E-02

4.400E-01 3.05E-03 8.02E-02 4.96E-03 8.82E-02 8.51E-02

4.500E-01 2.92E-03 7.95E-02 4.67E-03 8.71E-02 8.41E-02

4.600E-01 2,79E-03 7.88E-02 4.40E-03 8.60E-02 8.32E-02

4.700E-01 2.68E-03 7.81E-02 4.16E-03 8.50E-02 8.23E-02

4.800E-01 2.57E-03 7.75E-02 3.94E-03 8.40E-02 8.14E-02

4.900E-01 2.47E-03 7.68E-02 3.73E-03 8.30E-02 8.06E-02

5.000E-01 2.37E-03 7.62E-02 3.54E-03 8.21E-02 7.97E-02

108
Mold Material (alumina, silica, and zirconia mixture)

Constituents (Atomic Number:Fraction by Weight)

8:0.42080 13:0.27127 14:0.09067 40:0.21726

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02 3.19E-01 1.36E-01 1.70E+01 1.74E+01 1.71E+01

3.000E-02 1.76E-01 1.45E-01 5.67E+00 5.99E+00 5.82E+00

4.000E-02 1.13E-01 1.48E-01 2.54E+00 2.80E+00 2.69E+00

5.000E-02 7.79E-02 1.48E-01 1.34E+00 1.57E+00 1.49E+00

6.000E-02 5.70E-02 1.47E-01 7.94E-01 9.98E-01 9.41E-01

7.000E-02 4.35E-02 1.45E-01 5.07E-01 6.95E-01 6.52E-01

8.000E-02 3.44E-02 1.43E-01 3.42E-01 5.19E-01 4.85E-01

9.000E-02 2.79E-02 1.40E-01 2.42E-01 4.10E-01 3.82E-01

l.OOOE-01 2.31E-02 1.38E-01 1.77E-01 3.38E-01 3.15E-01

l.lOOE-01 1.94E-02 1.35E-01 1.33E-01 2.88E-01 2.69E-01

1.200E-01 1.66E-02 1.33E-01 1.03E-01 2.53E-01 2.36E-01

1.300E-01 1.43E-02 1.31E-01 8.13E-02 2.26E-01 2.12E-01

1.400E-01 1.25E-02 1.28E-01 6.52E-02 2.06E-01 1.93E-01

1.500E-01 l.lOE-02 1.26E-01 5.31E-02 1.90E-01 1.79E-01

1.600E-01 9.72E-03 1.24E-01 4.39E-02 1.78E-01 1.68E-01

1.700E-01 8.67E-03 1.22E-01 3.66E-02 1.67E-01 1.59E-01

1.800E-01 7.78E-03 1.20E-01 3.09E-02 1.59E-01 1.51E-01

1.900E-01 7.02E-03 1.18E-01 2.64E-02 1.52E-01 1.45E-01

2.000E-01 6.37E-03 1.16E-01 2.27E-02 1.45E-01 1.39E-01

2.100E-01 5.80E-03 1.15E-01 1.97E-02 1.40E-01 1.34E-01

2.200E-01 5.31E-03 1.13E-01 1.72E-02 1.35E-01 1.30E-01

2.300E-01 4.88E-03 l.llE-01 1.51E-02 1.31E-01 1.26E-01

2.400E-01 4.49E-03 l.lOE-01 1.33E-02 1.28E-01 1.23E-01

2.500E-01 4.15E-03 1.08E-01 1.18E-02 1.24E-01 1.20E-01

2.600E-01 3.85E-03 1.07E-01 1.06E-02 1.21E-01 1.18E-01

2.700E-01 3.58E-03 1.06E-01 9.48E-03 1.19E-01 1.15E-01

2.800E-01 3.34E-03 1.04E-01 8.54E-03 1.16E-01 1.13E-01

2.900E-01 3.12E-03 1.03E-01 7.73E-03 1.14E-01 l.llE-01

3.000E-01 2.92E-03 1.02E-01 7.02E-03 1.12E-01 1.09E-01

3.100E-01 2.74E-03 l.OlE-01 6.40E-03 l.lOE-01 1.07E-01

3.200E-01 2.57E-03 9.94E-02 5.85E-03 1.08E-01 1.05E-01

3.300E-01 2.42E-03 9.83E-02 5.37E-03 1.06E-01 1.04E-01

3.400E-01 2.29E-03 9.73E-02 4.94E-03 1.04E-01 1.02E-01

3.500E-01 2.16E-03 9.62E-02 4.56E-03 1.03E-01 l.OlE-01

3.600E-01 2.05E-03 9.52E-02 4.22E-03 l.OlE-01 9.94E-02

109
Mold Material (alumina, silica, and zirconia mixture)

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.700E-01 1.94E-03 9.42E-02 3.91E-03 l.OOE-01 9.81E-02

3.800E-01 1.84E-03 9.33E-02 3.64E-03 9.87E-02 9.69E-02

3.900E-01 1.75E-03 9.23E-02 3.39E-03 9.75E-02 9.57E-02

4.000E-01 1.67E-03 9.14E-02 3.16E-03 9.63E-02 9.46E-02

4.100E-01 1.59E-03 9.06E-02 2.96E-03 9.51E-02 9.35E-02

4.200E-01 1.51E-03 8.97E-02 2.78E-03 9.40E-02 9.25E-02

4.300E-01 1.45E-03 8.89E-02 2.61E-03 9.29E-02 9.15E-02

4.400E-01 1.38E-03 8.81E-02 2.45E-03 9.19E-02 9.05E-02

4.500E-01 1.32E-03 8.73E-02 2.31E-03 9.09E-02 8.96E-02

4.600E-01 1.27E-03 8.65E-02 2.18E-03 9.00E-02 8.87E-02

4.700E-01 1.21E-03 8.58E-02 2.06E-03 8.90E-02 8.78E-02

4.800E-01 1.16E-03 8.50E-02 1.95E-03 8.82E-02 8.70E-02

4.900E-01 1.12E-03 8.43E-02 1.85E-03 8.73E-02 8.62E-02

5.000E-01 1.07E-03 8.36E-02 1.76E-03 8.65E-02 8.54E-02

110
Molybdenum

Constituents (Atomic Number:Fraction by Weight)

42:1.00000

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02 9.89E-01 9.51E-02 7.85E+01 7.95E+01 7.86E+01

3.000E-02 5.58E-01 1.09E-01 2.74E+01 2.81E+01 2.75E+01

4.000E-02 3.64E-01 1.16E-01 1.25E+01 1.29E+01 1.26E+01

5.000E-02 2.54E-01 1.19E-01 6.67E+00 7.04E+00 6.79E+00

6.000E-02 1.87E-01 1.20E-01 3.97E+00 4.27E+00 4.09E+00

7.000E-02 1.44E-01 1.21E-01 2.55E+00 2.81E+00 2.67E+00

8.000E-02 1.14E-01 1.20E-01 1.73E+00 1.96E+00 1.85E+00

9.000E-02 9.30E-02 1.19E-01 1.23E+00 1.44E+00 1.34E+00

l.OOOE-01 7.73E-02 1.18E-01 9.01E-01 l.lOE+00 1.02E+00

l.lOOE-01 6.53E-02 1.16E-01 6.81E-01 8.63E-01 7.97E-01

1.200E-01 5.60E-02 1.15E-01 5.27E-01 6.98E-01 6.42E-01

1.300E-01 4.85E-02 1.13E-01 4.16E-01 5.78E-01 5.30E-01

1.400E-01 4.24E-02 1.12E-01 3.35E-01 4.89E-01 4.46E-01

I.500E-01 3.74E-02 l.lOE-01 2.73E-01 4.21E-01 3.83E-01

1.600E-01 3.32E-02 1.09E-01 2.26E-01 3.68E-01 3.35E-01

1.700E-01 2.97E-02 1.07E-01 1.89E-01 3.26E-01 2.96E-01

1.800E-01 2.67E-02 1.06E-01 1.60E-01 2.92E-01 2.66E-01

1.900E-01 2.41E-02 1.04E-01 1.37E-01 2.65E-01 2.41E-0I

2.000E-01 2.19E-02 1.03E-01 1.18E-01 2.42E-01 2.20E-01

2.100E-01 2.00E-02 1.02E-01 1.02E-01 2.23E-01 2.03E-01

2.200E-01 1.83E-02 l.OOE-01 8.90E-02 2.08E-01 1.89E-01

2.300E-01 1.68E-02 9.90E-02 7.83E-02 1.94E-01 1.77E-01

2.400E-01 1.55E-02 9.77E-02 6.92E-02 1.82E-01 1.67E-01

2.500E-01 1.44E-02 9.65E-02 6.16E-02 1.72E-01 1.58E-01

2.600E-01 1.33E-02 9.54E-02 5.50E-02 1.64E-01 1.50E-01

2.700E-01 1.24E-02 9.42E-02 4.94E-02 1.56E-01 1.44E-01

2.800E-01 1.16E-02 9.32E-02 4.45E-02 1.49E-01 1.38E-01

2.900E-01 1.08E-02 9.21E-02 4.03E-02 1.43E-01 1.32E-01

3.000E-01 l.OlE-02 9.11E-02 3.67E-02 1.38E-01 1.28E-01

3.100E-01 9.52E-03 9.01E-02 3.34E-02 1.33E-01 1.24E-01

3.200E-01 8.96E-03 8.91E-02 3.06E-02 1.29E-01 1.20E-01

3.300E-01 8.44E-03 8.82E-02 2.81E-02 1.25E-01 1.16E-01

3.400E-01 7.97E-03 8.73E-02 2.59E-02 1.2IE-01 1.13E-01

3.500E-01 7.53E-03 8.64E-02 2.39E-02 1.18E-01 l.lOE-01

3.600E-01 7. 14E-03 8.55E-02 2.21E-02 1.15E-01 1.08E-01

111
Molybdenum

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.700E-01 6.77E-03 8.47E-02 2.05E-02 1.12E-01 1.05E-01

3.800E-01 6.43E-03 8.39E-02 1.91E-02 1.09E-01 1.03E-01

3.900E-01 6.11E-03 8.31E-02 1.78E-02 1.07E-01 l.OlE-01

4.000E-01 5.82E-03 8.23E-02 1.66E-02 1.05E-01 9.89E-02

4.100E-01 5.54E-03 8.15E-02 1.55E-02 1.03E-01 9.71E-02

4.200E-01 5.29E-03 8.08E-02 1.46E-02 l.OlE-01 9.54E-02

4.300E-01 5.05E-03 8.01E-02 1.37E-02 9.88E-02 9.38E-02

4.400E-01 4.83E-03 7.94E-02 1.29E-02 9.71E-02 9.23E-02

4.500E-01 4.62E-03 7.87E-02 1.22E-02 9.54E-02 9.08E-02

4.600E-01 4.43E-03 7.80E-02 1.15E-02 9.39E-02 8.95E-02

4.700E-01 4.25E-03 7.73E-02 1.09E-02 9.24E-02 8.82E-02

4.800E-01 4.08E-03 7.67E-02 1.03E-02 9.11E-02 8.70E-02

4.900E-01 3.92E-03 7.61E-02 9.75E-03 8.97E-02 8.58E-02

5.000E-01 3.76E-03 7.54E-02 9.26E-03 8.85E-02 8.47E-02

112
Nickel

Constituents (Atomic Number:Fraction by Weight)

28:1.00000

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02 5.95E-01 1.16E-01 3.15E+01 3.22E+01 3.16E+01

3.000E-02 3.30E-01 1.30E-01 9.88E+00 1.03E+01 l.OOE+01

4.000E-02 2.08E-01 1.36E-01 4.26E+00 4.60E+00 4.39E+00

5.000E-02 1.44E-01 1.38E-01 2.19E+00 2.47E+00 2.33E+00

6.000E-02 1.06E-01 1.38E-01 1.27E+00 1.51E+00 1.41E+00

7.000E-02 8.17E-02 1.37E-01 7.95E-01 l.OlE+00 9.32E-01

8.000E-02 6.48E-02 1.36E-01 5.30E-01 7.31E-01 6.66E-01

9.000E-02 5.27E-02 1.34E-01 3.70E-01 5.57E-01 5.04E-01

l.OOOE-01 4.37E-02 1.32E-01 2.68E-01 4.44E-01 4.00E-01

l.lOOE-01 3.68E-02 1.30E-01 2.00E-01 3.67E-01 3.31E-01

1.200E-01 3.13E-02 1.28E-01 1.53E-01 3.13E-01 2.82E-01

1.300E-01 2.70E-02 1.26E-01 1.20E-01 2.73E-01 2.46E-01

1.400E-01 2.36E-02 1.25E-01 9.57E-02 2.44E-01 2.20E-01

1.500E-01 2.07E-02 1.23E-01 7.75E-02 2.21E-01 2.00E-01

1.600E-01 1.84E-02 1.21E-01 6.36E-02 2.03E-01 1.84E-01

1.700E-01 1.64E-02 1.19E-01 5.29E-02 1.88E-01 1.72E-01

1.800E-01 1.47E-02 1.17E-01 4.44E-02 1.76E-01 1.62E-01

1.900E-01 1.33E-02 1.16E-0] 3.77E-02 1.67E-01 1.53E-01

2.000E-01 1.20E-02 1.14E-01 3.23E-02 1.58E-01 1.46E-01

2.100E-01 l.lOE-02 1.12E-01 2.79E-02 1.51E-01 1.40E-01

2.200E-01 l.OOE-02 l.llE-01 2.42E-02 1.45E-01 1.35E-01

2.300E-01 9.20E-03 1.09E-01 2.12E-02 1.40E-01 1.31E-01

2.400E-01 8.48E-03 1.08E-01 1.87E-02 1.35E-01 1.27E-01

2.500E-01 7.84E-03 1.06E-01 1.66E-02 1.31E-01 1.23E-01

2.600E-01 7.27E-03 1.05E-01 1.47E-02 1.27E-01 1.20E-01

2.700E-01 6.76E-03 1.04E-01 1.32E-02 1.24E-01 1.17E-01

2.800E-01 6.30E-03 1.03E-01 1.19E-02 1.21E-0I I.14E-01

2.900E-01 5.88E-03 l.OlE-01 1.07E-02 1.18E-01 1.12E-01

3.000E-01 5.51E-03 l.OOE-01 9.70E-03 1.15E-01 l.lOE-01

3.100E-01 5.17E-03 9.90E-02 8.82E-03 1.13E-01 1.08E-01

3.200E-01 4.86E-03 9.79E-02 8.05E-03 l.llE-01 1.06E-01

3.300E-01 4.58E-03 9.69E-02 7.38E-03 1.09E-01 1.04E-01

3.400E-01 4.32E-03 9.58E-02 6.77E-03 1.07E-01 1.03E-01

3.500E-01 4.08E-03 9.48E-02 6.24E-03 1.05E-01 l.OlE-01

3.600E-01 3.86E-03 9.38E-02 5.76E-03 1.03E-01 9.96E-02

113
Nickel

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.700E-01 3.66E-03 9.29E-02 5.34E-03 1.02E-01 9.82E-02

3.800E-01 3.48E-03 9.20E-02 4.96E-03 l.OOE-01 9.69E-02

3.900E-01 3.30E-03 9.11E-02 4.61E-03 9.90E-02 9.57E-02

4.000E-01 3.14E-03 9.02E-02 4.30E-03 9.76E-02 9.45E-02

4.100E-01 2.99E-03 8.94E-02 4.02E-03 9.64E-02 9.34E-02

4.200E-01 2.86E-03 8.85E-02 3.76E-03 9.51E-02 9.23E-02

4.300E-01 2.73E-03 8.77E-02 3.53E-03 9.40E-02 9.12E-02

4.400E-01 2.61E-03 8.69E-02 3.32E-03 9.29E-02 9.02E-02

4.500E-01 2.49E-03 8.62E-02 3.12E-03 9.18E-02 8.93E-02

4.600E-01 2.39E-03 8.54E-02 2.94E-03 9.07E-02 8.84E-02

4.700E-01 2.29E-03 8.47E-02 2.78E-03 8.98E-02 8.75E-02

4.800E-01 2.20E-03 8.40E-02 2.63E-03 8.88E-02 8.66E-02

4.900E-01 2.11E-03 8.33E-02 2.49E-03 8.79E-02 8.58E-02

5.000E-01 2.03E-03 8.26E-02 2.37E-03 8.70E-02 8.50E-02

114
N5 (nickel superalloy)

Constituents (Atomic Number:Fraction by Weight)

13:0.06200 24:0.07000 27:0.07500 28:0.63300 42:0.01500 73:0.06500

74:0.05000 75:0.03000

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02 7.70E-01 l.llE-01 3.39E+01 3.48E+01 3.40E+01

3.000E-02 4.38E-01 1.24E-01 1.09E+01 1.14E+01 l.lOE+01

4.000E-02 2.81E-01 1.30E-01 4.76E+00 5.17E+00 4.89E+00

5.000E-02 1.96E-01 1.32E-01 2.49E+00 2.82E+00 2.62E+00

6.000E-02 1.46E-01 1.32E-01 1.46E+00 1.74E+00 1.59E+00

7.000E-02 1.13E-01 1.32E-01 1.89E+00 2.14E+00 2.02E+00

8.000E-02 9.00E-02 1.31E-01 1.49E+00 1.71E+00 1.62E+00

9.000E-02 7.35E-02 1.29E-01 1.08E+00 1.28E+00 1.21E+00

l.OOOE-01 6.11E-02 1.28E-01 8.10E-01 9.99E-01 9.38E-01

l.lOOE-01 5.16E-02 1.26E-01 6.23E-01 8.00E-01 7.49E-01

1.200E-01 4.41E-02 1.24E-01 4.89E-01 6.57E-01 6.13E-01

1.300E-01 3.81E-02 1.22E-01 3.91E-01 5.51E-01 5.13E-01

1.400E-01 3.33E-02 1.20E-01 3.18E-01 4.72E-01 4.38E-01

1.500E-01 2.94E-02 1.18E-01 2.62E-01 4.10E-01 3.81E-01

1.600E-01 2.61E-02 1.17E-01 2.19E-01 3.62E-01 3.36E-01

1.700E-01 2.33E-02 1.15E-01 1.85E-01 3.23E-01 3.00E-01

1.800E-01 2.10E-02 1.13E-01 1.58E-01 2.92E-01 2.71E-01

1.900E-01 1.90E-02 1.12E-01 1.36E-01 2.66E-01 2.47E-01

2.000E-01 1.72E-02 l.lOE-01 1.18E-01 2.45E-01 2.28E-01

2.100E-01 1.57E-02 1.09E-01 1.03E-01 2.27E-01 2.11E-01

2.200E-01 1.44E-02 1.07E-01 9.04E-02 2.12E-01 1.98E-01

2.300E-01 1.33E-02 1.06E-01 8.00E-02 1.99E-01 1.86E-01

2.400E-01 1.22E-02 1.04E-01 7.12E-02 1.88E-01 1.76E-01

2.500E-01 1.13E-02 1.03E-01 6.36E-02 1.78E-01 1.67E-01

2.600E-01 1.05E-02 1.02E-01 5.72E-02 1.70E-01 1.59E-01

2.700E-01 9.80E-03 l.OlE-01 5.16E-02 1.62E-01 1.52E-01

2.800E-01 9.15E-03 9.93E-02 4.68E-02 1.55E-01 1.46E-01

2.900E-01 8.56E-03 9.82E-02 4.26E-02 1.49E-01 1.41E-01

3.000E-01 8.02E-03 9.71E-02 3.88E-02 1.44E-01 1.36E-01

3.100E-01 7.54E-03 9.60E-02 3.56E-02 1.39E-01 1.32E-01

3.200E-01 7.09E-03 9.49E-02 3.27E-02 1.35E-01 1.28E-01

3.300E-01 6.69E-03 9.39E-02 3.01E-02 1.31E-01 1.24E-01

3.400E-01 6.31E-03 9.29E-02 2.79E-02 1.27E-01 1.21E-01

3.500E-01 5.97E-03 9.19E-02 2.58E-02 1.24E-01 1.18E-01

115
N5 (nickel superalloy)

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.600E-01 5.66E-03 9.10E-02 2.40E-02 1.21E-01 1.15E-01

3.700E-01 5.37E-03 9.01E-02 2.23E-02 1.18E-01 1.12E-01

3.800E-01 5.10E-03 8.92E-02 2.08E-02 1.15E-01 l.lOE-01

3.900E-01 4.85E-03 8.83E-02 1.95E-02 1.13E-01 1.08E-01

4.000E-01 4.62E-03 8.75E-02 1.83E-02 l.lOE-01 1.06E-01

4.100E-01 4.40E-03 8.66E-02 1.71E-02 1.08E-01 1.04E-01

4.200E-01 4.20E-03 8.58E-02 1.61E-02 1.06E-01 1.02E-01

4.300E-01 4.01E-03 8.51E-02 1.52E-02 1.04E-01 l.OOE-01

4.400E-01 3.84E-03 8.43E-02 1.43E-02 1.02E-01 9.86E-02

4.500E-01 3.67E-03 8.36E-02 1.36E-02 l.OlE-01 9.71E-02

4.600E-01 3.52E-03 8.28E-02 1.28E-02 9.92E-02 9.57E-02

4.700E-01 3.38E-03 8.21E-02 1.22E-02 9.77E-02 9.43E-02

4.800E-01 3.24E-03 8.15E-02 1.15E-02 9.62E-02 9.30E-02

4.900E-01 3.11E-03 8.08E-02 l.lOE-02 9.49E-02 9.18E-02

5.000E-01 2.99E-03 8.01E-02 1.04E-02 9.36E-02 9.06E-02

116
Tungsten

Constituents (Atomic Number:Fraction by Weight)

74:1.00000

Partial Interaction Coefficients and Total Attenuation Coefficients

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

2.000E-02 2.04E+00 7.25E-02 6.36E+01 6.57E+01 6.37E+01

3.000E-02 1.20E+00 8.64E-02 2.14E+01 2.27E+01 2.15E+01

4.000E-02 7.94E-01 9.43E-02 9.78E+00 1.07E+01 9.87E+00

5.000E-02 5.61E-01 9.86E-02 5.29E+00 5.95E+00 5.39E+00

6.000E-02 4.21E-01 l.OlE-01 3.19E+00 3.71E+00 3.29E+00

7.000E-02 3.28E-01 1.02E-01 1.06E+01 l.lOE+01 1.07E+01

8.000E-02 2.64E-01 1.03E-01 7.44E+00 7.81E+00 7.54E+00

9.000E-02 2.17E-01 1.02E-01 5.47E+00 5.79E+00 5.57E+00

l.OOOE-01 1.81E-01 1.02E-01 4.15E+00 4.44E+00 4.26E+00

l.lOOE-01 1.54E-01 l.OlE-01 3.23E+00 3.48E+00 3.33E+00

1.200E-01 1.32E-01 l.OOE-01 2.55E+00 2.79E+00 2.66E+00

1.300E-01 1.15E-01 9.95E-02 2.06E+00 2.27E+00 2.16E+00

1.400E-01 l.OOE-01 9.85E-02 1.68E+00 1.88E+00 1.78E+00

1.500E-01 8.88E-02 9.74E-02 1.40E+00 1.58E+00 1.49E+00

1.600E-01 7.91E-02 9.63E-02 1.17E+00 1.35E+00 1.27E+00

1.700E-01 7.09E-02 9.52E-02 9.93E-01 1.16E+00 1.09E+00

1.800E-01 6.40E-02 9.40E-02 8.51E-01 l.OlE+00 9.45E-01

1.900E-01 5.80E-02 9.29E-02 7.35E-01 8.86E-01 8.28E-01

2.000E-01 5.29E-02 9.18E-02 6.40E-01 7.84E-01 7.32E-01

2.100E-01 4.84E-02 9.08E-02 5.61E-01 7.00E-01 6.52E-01

2.200E-01 4.45E-02 8.97E-02 4.95E-01 6.29E-01 5.84E-01

2.300E-01 4.10E-02 8.87E-02 4.39E-01 5.69E-01 5.28E-01

2.400E-01 3.79E-02 8.77E-02 3.92E-01 5.17E-01 4.79E-01

2.500E-01 3.52E-02 8.67E-02 3.51E-01 4.73E-01 4.38E-01

2.600E-01 3.27E-02 8.57E-02 3.16E-01 4.35E-01 4.02E-01

2.700E-01 3.05E-02 8.48E-02 2.86E-01 4.01E-01 3.71E-01

2.800E-01 2.86E-02 8.39E-02 2.60E-01 3.72E-01 3.44E-01

2.900E-01 2.68E-02 8.30E-02 2.37E-01 3.47E-01 3.20E-01

3.000E-01 2.51E-02 8.21E-02 2.17E-01 3.24E-01 2.99E-01

3.100E-01 2.36E-02 8.13E-02 1.99E-01 3.04E-01 2.80E-01

3.200E-01 2.23E-02 8.05E-02 1.83E-01 2.86E-01 2.63E-01

3.300E-01 2.10E-02 7.97E-02 1.69E-01 2.70E-01 2.49E-01

3.400E-01 1.99E-02 7.89E-02 1.56E-01 2.55E-01 2.35E-01

3.500E-01 1.88E-02 7.81E-02 1.45E-01 2.42E-01 2.23E-01

3.600E-01 1.78E-02 7.74E-02 1.35E-01 2.30E-01 2.12E-01

117
Tungsten

Photon TOTAL

Energy coh Comp PE w/coh w/o coh

(MeV) (cm2/g) (cm2/g) (cm2/g) (cm2/g) (cm2/g)

3.700E-01 1.69E-02 7.66E-02 1.26E-01 2.19E-01 2.02E-01

3.800E-01 1.61E-02 7.59E-02 1.18E-01 2.10E-01 1.94E-01

3.900E-01 1.53E-02 7.53E-02 l.lOE-01 2.01E-01 1.85E-01

4.000E-01 1.46E-02 7.46E-02 1.03E-01 1.92E-01 1.78E-01

4.100E-01 1.39E-02 7.39E-02 9.71E-02 1.85E-01 1.71E-01

4.200E-01 1.33E-02 7.33E-02 9.14E-02 1.78E-01 1.65E-01

4.300E-01 1.27E-02 7.27E-02 8.62E-02 1.72E-01 1.59E-01

4.400E-01 1.22E-02 7.21E-02 8.14E-02 1.66E-01 1.53E-01

4.500E-01 1.17E-02 7.15E-02 7.71E-02 1.60E-01 1.49E-01

4.600E-01 1.12E-02 7.09E-02 7.30E-02 1.55E-01 1.44E-01

4.700E-01 1.07E-02 7.03E-02 6.93E-02 1.50E-01 1.40E-01

4.800E-01 1.03E-02 6.97E-02 6.58E-02 1.46E-01 1.36E-01

4.900E-01 9.91E-03 6.92E-02 6.26E-02 1.42E-01 1.32E-01

5.000E-01 9.54E-03 6.87E-02 5.96E-02 1.38E-01 1.28E-01

118
2.7x10' 2.567x10' 2.385x10' 660

8.96x10' 8.404x10' 8.000 X 10' 1083

5.91 X 10' 5.91 X 10' 6.09x10' 29.8

8.9 X 10' 8.304x10' 7.905 X 10' 1455

10.2 Physical Properties of Metals Used in the XRD Experiments

Density at Density at Melting

Atomic Density (kg m"') Solidus Liquidus Temperature

Metal Number at 20 °C (kg m'') (kg m"') (°C)

Aluminum 13

(Al)

Copper 29

(Cu)

Gallium 3

1

(Ga)

Nickel 28

(Ni)

10.3 Composition of N5 Nickel Alloy

In weight percent, this is the approximate composition for the major elements.

7.0% Cr

7.5% Co

1.5% Mo

6.2% Al

6.5% Ta

5.0% W

3.0% Re

Balance is Ni

119
10.4 Anomalous Dispersion Corrections for Nickel

The factors fl and f2, for nickel, as a function of energy are tabulated below. The source of

this data is reference [25].

Ni: Z = 28

Atomic weight =58.69000 g/mol

Nominal density: 8. 876g/cm3

^a(barns/atom) = n(cm2/g) x 97.4571

E(eV) n(cm2/g) = f2(e/atom) x7 16993

Location (keV) of Absorption Edges:

K 8.33280E+00 LI 1.00810E+00 L II 8.71900E-01 L III 8.54700E-01

MI 1.11800E-01 Mil 6.81000E-02 Mill 6.81000E-02 M IV 3.60000E-03

MV 3.60000E-03

Relativistic correction estimate frel (H82,3/5CL) = -0. 12883 -0.081 e/atom

Nuclear Thomson correction fNT = -0.0073281 e/atom

E fl f2

(keV) (e/atom) (e/atom)

2.080733 27.9855 5.1095

2.224304 28.0289 4.592

2.377781 28.0405 4.1285

2.541848 28.0299 3.7138

2.717235 28.0016 3.343

2.904724 27.9659 3.0114

3.10515 27.9386 2.6981

3.319406 27.8847 2.4055

3.548445 27.8165 2.1392

3.793288 27.734 1.897

4.055024 27.6425 1.6844

4.334821 27.5458 1.4976

4.633924 27.4435 1.3269

4.953664 27.3322 1.1761

5.295467 27.2114 1.0433

5.660855 27.0779 0.92645

6.051453 26.9254 0.82342

6.469004 26.7418 0.73254

6.915365 26.5023 0.65229

7.392525 26.1454 0.58138

E fl f2

(keV) (e/atom) (e/atom)

7.902609 25.4382 0.51866

8.166144 24.5187 0.49051

8.291136 23.0862 0.47804

8.324467 21.3577 0.4748

8.374464 23.1229 3.8783

8.44789 24.2866 3.8127

8.499456 24.7181 3.7677

9.030794 26.3786 3.4017

9.653919 27.1216 3.0709

10.32004 27.5654 2.7492

11.03212 27.8453 2.4485

11.79334 28.0311 2.1838

12.60708 28.1583 1.9478

13.47697 28.2454 1.7376

14.40688 28.3043 1.5502

15.40095 28.3432 1.3831

16.46362 28.3682 1.2341

17.59961 28.4192 1.0942

18.81398 28.4194 0.96902

20.11215 28.412 0.8582

120

\
E fl f2

(keV) (e/atom) (e/atom)

21.500 28.400 0.76013

22.983 28.384 0.67282

24.569 28.366 0.59559

26.265 28.348 0.52725

28.077 28.329 0.46461

30.014 28.309 0.40881

32.085 28.288 0.35972

34.299 28.268 0.31655

36.666 28.248 0.27821

39.195 28.230 0.24347

41.900 28.211 0.21307

44.791 28.193 0.18647

47.882 28.177 0.1632

51.185 28.161 0.14284

54.717 28.147 0.12502

58.493 28.133 0.10943

62.529 28.121 0.095778

66.843 28.110 0.083836

71.455 28.099 0.073385

76.386 28.090 0.064239

81.656 28.081 0.056155

87.291 28.073 0.048934

93.314 28.066 0.042642

99.752 28.060 0.037161

106.635 28.054 0.032385

113.993 28.048 0.028224

E fl f2

(keV) (e/atom) (e/atom)

121.859 28.043 0.024598

130.267 28.039 0.021438

139.255 28.035 0.018685

148.864 28.031 0.016286

159.136 28.028 0.014196

170.116 28.025 0.012374

181.854 28.022 0.010786

194.402 28.020 0.009402

207.816 28.018 0.008196

222.155 28.016 0.0071448

237.484 28.014 0.0062286

253.870 28.013 0.00543

271.387 28.011 0.0047339

290.113 28.010 0.0041272

310.130 28.009 0.0035983

331.529 28.008 0.0031373

354.405 28.007 0.0027354

378.859 28.006 0.002385

405.000 28.006 0.0020796

432.945 28.005 0.0018133

121
10.5 Model of Transmission XRD from a Sample Surrounded by Mold Material

Example: Nickel sample with Refractory Oxide Mold Walls File: XRDEFNI3.MCD

I0:=10^ Wl : = 0.6 W2 =0.6 NL:=1000 L:=1.0 dx^ —NL

ps =8.9 density of Ni (g/cm^)

pw =2.46 density of Mold Material (g/cm^)

K is the forward scattering factor, the fraction of coherently scattered photons scattered

into the area occupied by the x-ray imager.

D is the imager diameter, SID is the source-to-imager distance

D:=50 SID =150

D

isroi

, 2 , atan 6 = 0.165

Sin

R:= R= 152.069 h: = R-SID h = 2.069

cos(9)

K: = Jl- K = 6.803*10^

2R

i:=l.. 49

Energy (keV) E. :=READ( "energys.dat") Coherent jisr. :=READ( "nicoh.dat") Atten in Sample

Total Atten ust. : = READ( "nitot.dat" ) Total Atten jiwt. : = READ( "hmoldtot.dat"

)

in Sample in Mold Wall

Attenuation coefficients are mass attenuation coefficients (cm2/g). Multiply these by the

density to find the linear attenuation coefficients.

122
MODEL OF RADIATION TRANSPORT

IN X-RAY DIFFRACTION SENSOR EXPERIMENTS

MOLD

WALLS

>^

SAMPLE

X-RAY

SOURCE

TO IMAGER

^ W L -> W2

-^

I0| is the intensity (at energy E,) of the x-ray beam, with no sample or mold present.

Hj is the intensity transmitted through the entrance mold wall.

-HwtipwWl

II. : = IOe

I (A1)

l^r •RAY TRANSMISSION THROUGH ENTRANCE MOLD

73 0.9 1

0.8 8

i

0.7

11. 0.6

1 am 10 0.5 -a3

0.4 o

0.3

[-~i a 0.2 o

"3 0.1

ea

Li. 0.1 0.2 0.3 0.4 0.5 E. X-Ray Energy (MeV)

I2i is the intensity of coherent (Rayleigh) scatter which exits from the sample. It is a integral of

the product of (1) the attenuation in the sample up to the point of coherent scatter, (2) the

efficiency of generation of coherent scatter, and (3) the attenuation of the coherent scatter as it emerges from the sample.

123
NL

n=l

|J5ti-psndx / -nsri-ps-dx\ -M5tiPs(L- (n-dx)) •K-ll - e j-e (A2)

Symbolically simplfying eq. (2) yields:

12. : = -Il.-K-NL-r-exp[-fist.-ps-L] +• exp[-ps-fnst.-L+ jisr.-dxHl (A3)

Considers Sample

& Entrance Mold ->

1

10

I.S'IO"'*

Lias'io""*

7.5no"^

3.75«10"^

o

IS /^

/ \

/

"v"^

1

_J.

0.1 0.2 0.3 0.4

X-Ray Energy (MeV)

Considers Sample

Only >

i

I

V3I

g

'5b I

II.

•in ** 2*10

1.5*10

5*10

X-Ray Energy (MeV)

124
13(E) is the intensity of coherent scatter which is transmitted through the exit mold wall.

-HWtjpwW2 (A4)

13. : = I2.e

I t

•in '*

6W

oU

[Jh

13.

1

1.5*10

mo

in ^ 5*10

0.1 0.2 0.3 E.

I X-Ray Energy(MeV)

0.5

13. WRITE( "ni6 1 00h6.dat" ) : = —

10

Calculate the intensity in the primary beam transmitted through both mold walls and the sample.

The transmitted primary beam is what would normally be used to form a radiographic image.

-jiwtj-pw-Wl -^st:-ps-L -(iwt;-pw-'W2

It. : = IOe e e

I (A5)

« K; CQ^

10

CL,

<^-l Oa

o

<jCS

0.7

0.6

0.5

0.4

0.3

0.2

0.1

PRIMARY BEAM TRANSMISSION

0.1 0.2 0.3 Ej X-Ray Energy (keV)

0.4 0.5

The plots are for a 6 mm entrance mold, 10 mm Ni sample, and a 6 mm exit mold.

125
Fundamental Physics Model

File: XRDEFF10 - fig 23.MCD

As an x-ray beam travels tiirough the mold and a crystalline specimen,

attenuation and diffraction will occur.

Attenuation of a narrow, monochromatic x-ray beam follows the relation

-Jl'PX I^Io'e" (1)

where

I is the intensity after passing through the material,

lo is the incident intensity,

ji/p is the mass attenuation coefficient (material and energy dependent),

p is the density of the material, and

X is the thickness of the material.

The intensity of x-rays diffracted by a small crystal is given by [Warren, eqn (3.6), p 29]

I

eO'* W 1 \^ [l + cos^(2-e)]

d

° R'-mO^-c' \4-^-e0

2 VT'^2 KT->2 I. :=!• — • -^^ ^ ^^-F-F'-Nr-Na-Na^ (2)

where

Id is the diffracted intensity,

lo is the incident intensity,

eO is the charge of an electron,

R is the distance from the origin of diffraction to a point of observation,

mO is the mass of an electron, c is the speed of light, eO is the permittivity of free space,

29 is the angle between the incident and diffracted beams,

F is the stnjcture factor of the crystal, and F" is its complex conjugate,

N1, N2, and N3 are the number of unit cells in the small crystal (along the

directions of the crystal axes).

The integrated intensity (total diffracted energy) from a small crystal is given by [Warren, eqn (4.6), p 44]

DifiEn:=^.(^.(_^f.Ii±^^!^ili2l.F.F.X^^' (3) w \mO^-c^l \4-Ji-^/ 2-sin(2-e) va^

where

CO is the angular velocity that the primary beam rotates (required to integrate through

the area under the interference function sin2(Ny)/sin2(y),

V Is the volume of the small crystal, and

va is the volume of the unit cell.

126
Physical Constants

Planck's constant Mass of an Electron Speed of Light

h:= 6.6260755- 10'^'*-joulesec mO := 9.1093897- 10"^^-kg c =299792458-—

sec

Pernnittivity of vacuum Charge of an Electron Energy = mO c^

£0=8.854187817-10-'^- . i<m 177^1 in- 19 , x: QiQ7iiin"14 .2-2 jjj eO = 1.6021773310 -coul Energy = 8.1871 1*10 •kg'm 'sec

Example: Single-Crystal Nickel Specimen Surrounded by Refractory Oxide Mold Walls

Mold wall thicknesses (m) Wl =0. W2 =0.

Density of Mold Material (kg/m^) pw =2.46-10^

Thickness of specimen (m) L = 10. 10"^

Density of Ni (kg/m3) ps =8.9-10^

Divide the specimen into a number of segments NL = 10000

Length of a segment (cm) Ax = — Ax =1*10

NL

Lattice constant (length of an edge in the a =3.524 10'^°

unit cell) for Ni (m)

Atomic Number of Nickel Z = 28

Read in the energy points i = 1 .. 49

E. : = READ( "energys.dat" ) Energy (MeV)

E. : = E.1000 Convert to (keV) E = 100

, 12.398424468 ,

• /a , n * tr • ... xa 1 m-^^oo X. = >t IS in (Angstroms), for E in (keV) X- = 0.12398

' E.^

1

X. :=X.-10-^° Convert ?. to (m). X = 1.23984.10"^^ 11 ^ ' 9

Read in the incident x-ray source spectrum (flux per energy interval) at each of the energy points (Ej).

10. : = READ( "spect001.dat")

127
Read the attenuation coefficients at each energy point, for the mold material and the specimen.

Total Atten jiwt. : = READ( "hmoldtot.dat"

)

Total Atten fist. : = READ( "nitot.dat"

)

in Mold Wall ' in Sample

Attenuation coefficients are mass attenuation coefficients (cm^/g). Multiply

these by the density to get the linear attenuation coefficients.

nwt. fist, uwt. : = —- list.- —i Convert the units to (m2/kg). '10 '10

Choose a set of lattice planes in the crystal [Miller indices (hkl)]. This defines a particular "reflection" to investigate. The indices should be unmixed (nickel is fee) for F (structure factor) to be nonzero.

Let h:=l k:=l 1=1

The spacing of lattice planes, d, for a crystal of cubic symmetry is

—

1 (h^+k^+1^)' . ,., --^^

L where (4) d^ a^ a is the lattice constant.

Diffraction will occur when Bragg's

Law,

nX :=2dsin(e)' issatisfied. (5)

Substituting the expression for d (from (4) into Bragg's Law gives the scattering angle for a cubic crystal:

2 2, X /',2 ,2 ,2\ sin(e)^-^(h^ + k^+l

4a2

Note that:

2

^•) / ., -, ^\ 1 X- n, ^ ^ sine. sine.- IA!:i^.{h2 + k2+l2) or sine. : = l-iVhVk2+l^ ! i^^.Jh^k^ + l^ 4.a2

' 2 a ^ L 2-a

'

1

is independent of energy

/i A., rz I i\ igo

1/2 Scattering Q.: = asm\--—-'^h+k+r\ (6) Convert to degrees Theta.: = 6.- Angle (9)

' \2 a /

'

' n

Theta^= 1.74603

Scattering e2. : = 2e. radians

Angle, 20

128
26 is the scattering angle for a

given set of lattice planes and a given energy

(wavelength) x-ray.

Diffraction v^ill occur only if the

correct energy x-ray is incident on

the crystal at the correct angle.

For each energy considered, we

assume the specimen is con^ectly

aligned for diffraction. (2TheU)j

500

The structure factor F, is a function of the diffracting crystal material, its crystal structure, the particular

diffracting planes in the crystal, the incident x-ray energy, and the diffracted angle.

FN

E

n=l

f^.exp[i.2...(h.x^ + k.y^ + l.zj] (7)

where

fn is the atomic scattering factor of the nth atom in the unit cell

(it is a function of angle and energy),

(hkl) are the Miller indices of the diffracting planes,

x,y,z are the relative positions of the (N) atoms in the unit cell.

For a face-centered cubic (fee) crystal, F is zero if the indices (hkl) are mixed (even, odd)

and is 4*f if the indices are unmixed.

The atomic scattering factor, f, is a complex number.

fReal: = fO + fl+fNT + frel-Z' flmag: = f2' (8)

fO is a function of sin(0)/X, , fNT and frel can be considered constants, and

f1 and f2 are functions of energy

[CT Chantler, Theoretical form factor, attenuation, and scaatering tabulation for Z=1-92 from E=1-10eVto E=0.4-1 .OMeV, J. Chem. Ref. Data, Vol. 24, 71- (1995)]

129
Read in the coefficients for calculating the atomic scattering factor (fo) for the specimen material.

An empirical, sum of exponentials, fit is used [D.. Waasmaier, A Kirfel, New analytical scattering factor functions for free atoms and ions. Acta. Cryst. A, 151 , No. 3, 416-430 (1995)]. Aj, Bj, and C are the

coefficients in the fit.

j:=l.. 11 e. : = READ( "sfitni.dat")

j:=1..5

j: = 6.. 10

A. -e.

J J

B. .: = e. J-5 J

A^ = [0 13.52187 6.94728 3.86603 2.1359 4.28473]

B^ = [o 4.07728 0.28676 14.62263 71.96608 4.437«10"^

C =e

11 C = 2.7627

Read in the dispersion corrections to the atomic scattering factor.

fl . ; = READ( "fl vsENi.dat"

)

f2. : = READ( "f2vsENi.dat"

)

for Nickel —

>

fNT =-0.00733 frel : = -8.110-

To determine the atomic scattering factor for the specimen, first calculate the argument of the function.

sin9. arg. :: X.IO

1

10 arg^ = 0.24575

Note, X was converted to units of Angstrom in the equation above

arg:

0.246

0.2458

0.2456

0.2454 200 400 600

130
Calculate fO using an empirical fit

5

fD. := ) ; A..exp

j = l [-^yK)1 + c fO^ = 26.07104 (9)

26.1

fl.

28.6

28.4 -

28.2

500

c.

mo

0.01 -

500

fReal.Ill : = fD. + fl. + fNT + frel-Z flmag.^11: = f2. finagn. : = ^|(fReal.] + fflmag.

(10)

26.6 1 r

J \ \ L

"1 r

J L J L

50 100 150 200 250 300 350 400 450 500

131
The structure factor for an fee crystal, and lattice planes defined by unnnixed indices (hkl) is 4f . For

intensities, square the amplitude structure factor, (that is, 16 f2 ).

FF'. :=16(finagny (11)

FPj

1.12»10^

i.uno^

i.mo^

i.o9no" -

1.08»10^ 350 400 450 500

Beam Diameter (mm) D : = 1 .0 D - D 1

,2

-3

Beam area m^ BArea :=7i| —

,2

BArea = 7.85398' 10

Equivalent side of a square with the same area as the circular beam

A/BArea g=8.86227«10 ^ m

Length of a segment in therspecimen isdx (m). Ax =1*10

Number of unit cells across the beam cross section

Nl : = -? Nl = 2.514S3'10^ N2: = -5 N2-2.51483»10^

a

Ax "^ Number of unit cells alonadx N3 =_ N3 = 2.83768M0'' a

N1^N2^N3^ - 3.2208»10^^

132
Calculate the other quantities in eqn (3) to find the diffracted intensities.

eO W 1 \ =7_94079.io"3° -m^

imO'-cV \4-fs0

LP. : =

1

1 + (cos(2

2 •sin 2-0

Let 0) ;= 1

LP; 50 -

500

V::=BAreaAx V = 7.85398«10

-13

va:=a^ va = 4.37631 • 10 ^^

Diffin. :=^.[_^WJLr.i'^!!!ii:ili.FF..ay.^

® \mO^-c'*/ \4-n-£fl/ 2-sin(2- > \ '/ 2 va

(12)

DifiEn.

i

500

133
MODEL OF TRANSMISSION X-RAY DIFFRACTION

FOR A MOLD-ENCASED SINGLE-CRYSTAL

SPECIMEN

MOLD

WALLS

X-RAY

SOURCE

I0| Is the intensity (at energy E|) of the x-ray beam, with no sample or mold present.

Hi is the intensity transmitted through the entrance mold wall.

II. :=IO.expf-nwt.pwWl

(13)

. X-RAY TRANSMISSION THROUGH ENTRANCE MOLD 1.1

1.08

1.06

1.04

1.02

1 "

0.98

0.96

0.94

0.92

0.9

JJ •ii u.

,^ W- H 1

§

1

fe

1 00 2

X00 3Ray Energy (ke

00

V)

400 5

134
E2j is the total diffracted energy which emerges from the sample. It is the product of (1) the

attenuation in the sample up to the point of diffraction, (2) the efficiency of diffraction generation, and

(3) the attenuation of the diffracted x-rays as they exit through the remaining portion of the specimen.

These contributions from each segment of the specimen are summed over the path of the incident x-ray beam through the specimen.

n=0

NL ^(-usti-ps) n-Ax / ^4

mO^-c'*/ \4-7i-eO/ 2-sin(2

2 1 + cos 29.

•FF'.- I

3 BArea Ax -nstip8-{L-(nAx))

va

or

rL

E2. =11.

1 1

-Usq-psx / 4 e eO

mO^-c'*/ \4-7t-£0/ 2-sin(2-0.

1 \^ 1 -t-cos 2.e

I 3 BArea-dx -Msti.ps.(L-x)

-FF.fX.) • e dx (14) va

Move all terms which are not a function of n outside the sum.

E2.=I1..

1 1 \mO^-c^/ \4-n-^/ 2.sin(2-0_

I eO' \{ 1 \M^+^°K2'®i)';.pp..A N3BArea

va

-Ustj-psl'X e^ ^ ^ -M5tjps(L-x)

e dx

0)

Solve the integral

E2. : = — 11 eO" 1 + COS 2.e.

3 B^^ea exp -nst..ps-L

" 32 '' [rn0'.[,\{nW)]] sm(2.e.

'U- ¥¥'.%

> \ >/ 2 va

•L-- (15)

135
Considers Sample

& Entrance Mold ->

u3

^

0.001

E2.

•in '* BAreajQ 5*10

X-Ray Energy (keV)

Considers Sample

Only >

^

7.5*10

0.001

•in "*

E2.

BArea „

5*10

2.5*10

^

200

Ej X-Ray Energy (keV)

500

136
The diffracted energy is attenuated as it passes tlirougii the exit mold wall.

E3. ; = E2.-exp(-jiwt.-pwW2) (16)

0.001 r^

E3. BArea ,„

5 '10

X-Ray Energy (keV)

WRITEPRN( "pfhi 1 0.dat" ) : =

-

E3.

BArealO.

Calculate the intensity in the primary beam transmitted through both mold walls and the sample.

The transmitted primary beam is what would normally be used to form a radiographic image.

It. : = IO.exp(- nwt.pwWl Vexpf- nst.psL]exp[- nwt.pwW2 (17)

PRIMARY BEAM TRANSMISSION

X-Ray Energy (keV)

The plots are for a mm entrance mold, 10 mm Ni sample, and a mm exit mold.

500

137
10.6 Patent

United States Patent [i9] Siewert et al.

lilillllilliiilil

US005589690A

[11] Patent Number:

[451 Date of Patent;

5,589,690

Dec. 31, 1996

[54] APPARATUS AND METHOD FOR

MONITORESG CASTCV'G PROCESS

[75] Inventors; Thomas A. Siewert. Boulder: William

P. Dube, Denver: Dale W. Fitting,

Golden, all of Colo.

[73] Assignee: .National Institute of Standards and

Technology, Washington. D.C.

[21] Appl. No.: 407,699

[22] Filed: Mar. 21, 1995

[51] Int. Cl.° GOIN 23/20

[52] U.S. CI 250/390.06; 250/390.09:

378/71

[58] Field of Search 378/70.73,86,

378/71, 6; 250/390.09, 390.06

[56] References Cited

U.S. PATENT DOCUMENTS

3.499.736 3/1970 Zwaneburg 23/301 3.790.252 2/1974 Pao 350/160 R

3.833.810 9/1974 Efanov et ai 250/273

4.284.887 S/1981 Kusumoto et al 250/272

4,634,490 1/1987 Tacsumi et al 156/601 4.696.024 9/1987 Pesch 378/71

4.710.259 12/1987 Howe et al 156/601 5.016.266 5/1991 .Meumn 378/73

5.093.573 3/1992 Mikoshiba et al 250/310

5.136.624 8/1992 Schneider et al 378/73

5.193,104 3/1993 Basue et al 378/73 FOREIGN PATENT DOCUMENTS

642638 1/1979 U.S.S.R 378/73 OTHER PUBLICATIONS

"X-Ray Diffraction", Physical Metallursy Pnnciples by

Reed-Hill. pp. 26-33.

Baxter et al., "Rapid Orientation Measurement of Single

Crystal Casting Using 'Scorpio'". Insight, vol. 36. .No. 5. May 1994. Hashizume et al. 'Techniques for Time-Resolvcd X-Ray

Diffracdon' Using a Position Sensitive Counter". Japanese J. Appl. Phys., 15, (ID, Nov. 1976, pp. 2211-2219.

Primary Examiner—Carolyn E. Fields Attorney, Agent, or Firm—Shendan Ross & .Mcintosh

[57] ABSTRACT

The present invention uses a high energy x-ray, neutron, or gamma source for monitonng the intert'ace between a molten and solidified crystalline phase while in a furnace in a casting process. The radiation can also be used to determine

the quality and orientation of the crystals in the crystalline phase. The invention uses the disuncuve diffraction patterns produced by crystalline and amorphous phases to locate the

interface.

25 Claims, 4 Drawing Sheets

1,-— 50

u/ 42b

138
U.S. Patent Dec. 31, 1996 Sheet 1 of 4 5,589,690

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LL

139
U.S. Patent Dec. 31, 1996 Sheet 2 of 4 5,589,690

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CD

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oo

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c

LU

DC

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d)

Ll

CO

LLIO

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Q.

c

o

Q.

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oO

+c

oO

140
U.S. Patent Dec. 31, 1996 Sheet 3 of 4 5,589,690

o

o

CO

o

C\J

o

o

OvJ >

0) ^

CO

>.

o

ID CD O) 1

^— ««MM CI

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>s

03

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DC

1

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X

luej9L|oo SB 6u!6jeuj3 uoipejj

w

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141
U.S. Patent Dec. 31, 1996 Sheet 4 of 4 5,589,690

. t-^54a

r V ^58a

Fig. 4

<::. *^J

54b

V 58b

Fig. 5

90 100 110 120 130 140 150 160

X-Ray Energy (keV)

Fig. 6

142
5,589,690

SUMMARY OF THE INVENTION

20

APPARATUS AND METHOD FOR

MONITORING CASTING PROCESS

HELD OF THE INVENTION

5 The present invention relates generally to an apparatus and method for monitoring the casting or thermal treatment of materials, and more particularly, for monitoring the liquid amorphous/solid crystalline interface in a material being cast so as to permit process control parameters to be established lo and/or controlled in response thereto. BACKGROUND OF THE INVENTION

Advancements in materials processing technology have

caused an increasing demand for parts made from superailoys. Many high performance aircraft, for example, now

employ turbine blades that are single crystals of nickel- based superalloys. The desirability of superalloys results from their high strength at high operating temperatures. Superalloy parts are typically produced as single-crystal or directionally-solidified castings. Elaborate casting and

inspection methods are employed to ensure that each part is a single-crystal or directionally-solidified crystal with a desired orientation. Even minor defects in the crystalline 25 structure may be unacceptable as they can result in mechanical failure. To reduce the likelihood of defects in the crystalline

structure, the casting process for such parts has become a labor and time intensive process. The molten alloy is poured 30 into a mold located in a furnace. One end of the mold is cooled to initiate crystallization. The mold is then slowly withdrawn from the furnace. The withdrawal rate is extremely slow to ensure an acceptable crystallization rate and crystal of the correct orientation. A slow crystallization 35 rate promotes flawless crystal growth in the direction of

solidification. If the rate of crystallization is too rapid, the metal will form unacceptable polycrystals and the part must

be discarded. The possibility of forming parts with defects in the crystal structure with a lack of a reliable technique to 40 otherwise monitor the rate of crystal growth during casting has to date caused engineers to select extremely conservative (i.e., slow) crystallization rates. Further, despite the noted precautions taken during cast- ing, defects can still occur which result in discarded parts 45 and wasted production time. The scrapped material cannot simply be remelted and reused but must rather be retreated by an expensive refinement process before further use.

50

It is an objective of the present invention to provide an

apparatus and method for real time monitoring of the interface between the solid crystalline and liquid amorphous

phases of a material being cast in a mold during casting, 55 thereby allowing for an increase in throughput and decrease

in production costs. It is a related objective to provide a monitoring apparatus and method to permit casting process

control parameters to be established and/or controlled in response thereto, wherein the process provides optimal go conditions for the desired crystal formation.

It is a further specific objective to increase throughput and

decrease the production costs of single-crystal and directionally-solidified castings by decreasing the time required

to form such castings and minimizing the occurrence of 65 defects and flaws in the castings. As will be appreciated, the present invention is particularly useful for monitoring the

interface between molten (i.e., liquified) and solidified states of materials, such as alloys of iron, titanium, nickel, and aluminum, ceramics, semiconductors, such as silicon, ger- manium, gallium arsenide, cadmium telluride, cadmium

sulfi.de, and indium phosphide.

By way of initial summary, the present invention includes:

(i) directing source radiation through a casting mold and into an interface between a portion of the crystalline phase and amorphous phase of a material being cast to provide dif- fracted radiation having a first component associated with

the crystalline phase and a second component associated with the amorphous phase; (ii) receiving at least a portion of

at least one and preferably both of the first component and

second component of the diffracted radiation outside of tile casting mold and providing an output signal in response

thereto; and (iii) using the output signal to monitor the

interface between the crystalline and amorphous phases.

Preferably, x-ray radiation is employed and, as will be

further discussed, the energy and intensity of the source

radiation should be sufiBcient to penetrate the mold/cast

material and to otherwise provide the diffracted components

at an intensity sufEcieni for associated detection by a radiation-sensitive receiver means such as one or more x-ray imager(s) or energy detector(s). The casting mold can be composed of either amorphous or crystalline materials pro- vided that the container is penetrable by the source radiation and stable at the melting point of the cast material. Suitable container materials include, for example, sand, alumina,

zirconia, quartz, graphite, ceramics, and more particularly, aluminum oxide, zirconium oxide, and other metal oxides. Additional intervening structures, such as the walls of a

furnace, can be present between the radiation source and

diffracted radiation receiver, provided that such structures do

not block or otherwise unduly attenuate the source and/or

diffracted radiation. The first and second components of the diffracted radiation result from the differing manners in which the amor- phous phase and crystalline phase of the cast material

diffract the source radiation. Briefly, the crystalline phase

produces a radiation diffraction pattern comprising concentrated radiation areas, or high-intensity spots, while the amorphous phase produces a more diffuse and lower intensity ring pattern. Consequently, the radiation-sensitive receiver means should be positioned so as to receive at least a portion of one and preferably both of said concentrated

radiation and diffuse radiation associated with the crystalline and amorphous phases, respectively. In this manner, e.g., the output signal of the radiationsensitive receiver means will reflect, on a real-time basis, an

increase over lime in the received diffracted radiation associated with an increasing crystalline phase. More preferably,

e.g., by receiving a portion of both the diffracted radiation associated with an increasing crystalline phase and the

diffracted radiation associated with the decreasing amor- phous phase, the output signal can reflect the increase of the

diffracted radiation received from the crystalline phase rela- tive to that received from the amorphous phase. In this regard, the output signal, may include a first output signal component corresponding with the first diffracted radiation component that is received and a second output signal component corresponding with the second diffracted radiation component that is received. As will be appreciated then, use of the output signal to monitor the crystalline phase/amorphous phase interface generally entails (i) generating for successive time intervals corresponding successive values corresponding with at least

143
5,589,690

one or preferably both of a first output signal component

corresponding to the first difiFracted radiation component and

a second output signal component corresponding to the second diffracted radiation component; and (ii) employing

the successive values to monitor the state and/or progression 5 of the phase interface. More particularly, the successive

values can be compared to predetermined completion values

that correspond with associated degrees of crystalhzalion completion, as determined by prior design testing. For example, to determine the position of the interface as jq a function of time, the process can include the steps: (i) comparing during a first time interval the first and second

output signal components to locate the interface at a first position; (ii) comparing during a second time interval the

first and second output signal components to locate the

interface at a second position; and (iii) employing the first and second positions to monitor the phase interface. The

position of the interface can be estimated based upon the magnitude of the first and/or second output signal components. For example, the magnitude of the first output signal component can be compared to a predetermined magnitude ^^ corresponding with the diffraction pattern of a complete

crystalline phase in the mold and/or the magnitude of the second output component can be compared to a predeter- mined magnitude corresponding with the diffraction pattern of a complete amorphous phase in the mold to locate the 25 point below which the material in the container is substantially crystalline or above which the material in the container

is substantially amorphous.

Further, the above-noted successive values can be suc- cessively compared to either predetermined completion val- 30 ues or to each other to determine a rate of crystallization. Such determination may include, e.g., (i) comparing during

a first time interval a first output signal component (corre- sponding with the received portion of the first component of

the diffracted radiation) with a second output signal com- ,5 ponent (corresponding to the received portion of the second

signal component of the diffracted radiation) to provide a

first compared value; (ii) comparing during a second time

interval the first output signal component with the second

output signal component to provide a second compared

value; and (iii) employing the first and second compared

values to determine a rate of crystallization. The rate of

crystallization can be compared to predetermined rate values

to monitor when crystallization is complete (e.g., as rale approaches zero) and/or to otherwise monitor if crystalliza- tion is occurring at a desired rale (e.g., to ensure the desired 45 crystal structure). As will be appreciated, by monitoring the crystalline phase/amorphous phase interface, a monitor signal can be

generated for real-time control of at least one of the following casting process parameters: the temperature of a furnace 50 containing the mold and the rate of withdrawal of the cast material from the furnace. The present invention can be used not only to provide

real-time monitoring and control of a casting process but

also to verify in the laboratory casting process models 55 leading to the establishment of casting process control parameters to yield substantially optimal conditions for

crystal formation. The performance of casting under substantially optimal conditions reduces both the frequency of

defects and/or flaws in the crystal structure of the part and 60

the labor and time requirements to produce the part. These

reductions substantially reduce the production costs of the

parts relative to existing casting processes. BRIEF DESCRIPTION OF THE DRAWINGS

65 FIG. 1 illustrates one embodiment according of the present invention;

40

FIG. 2 is a plot of the mass attenuation coefiScients of

nickel versus the energy of the source radiation; FIG. 3 is a plot of the fraction of diffracted radiation emerging from a mold as coherent radiation as a function of

the energy of source radiation; FIGS. 4 and 5 depict diffraction patterns incident uf)on an

x-ray imager for a sample containing crystalline and amor- phous phases; and

FIG. 6 is a plot of the intensity detected by an energy

detector versus the energy of the source radiation at two time

intervals for a sample containing crystalline and amorphous

phases.

DETAILED DESCRIPTION

The present invention provides an apparatus and method

for the real-time monitoring of the interface between a

crystalline phase, such as a solidified metal, and an amor- phous phase, such as a molten metal, while contained in a mold. The interface is monitored by comparing the distinctly different radiation diffraction patterns produced by a crystalline phase compared to an amorphous phase. As discussed

in detail below, the highly ordered crystal structure of the

crystalline phase will produce a radiation diffraction pattern

that includes a number of distinct spots and energy peaks

while the relatively disordered structure of an amorphous

phase will produce a radiation diffraction pattern that is a

diffuse ring pattern with no distinct spots or energy peaks. Thus, the two phases produce radiation diffraction patterns

that are distinct in geometry, intensity, and energy distribution. Although materials in the mold can produce interfering spots or rings, the radiation diffraction pattern produced by

the mold is known, or is measurable, and can therefore be removed from or otherwise accounted for in the measured

diffraction pattern. FIG. 1 depicts an embodiment according to the present

invention. The embodiment includes an x-ray radiation source 10, a collimator 14, a beam stop 18, and a detector assembly 22. The radiation source 10 produces x-ray source

radiation 26 of a relatively high energy and intensity to penetrate a sample section 30, which includes the crystalline and amorphous phases 34, 38, and mold walls 42a,b. The

collimator 14 restricts the source radiation 26 to a narrow

range of angular orientations. This collimated radiation 46

has a plurality of substantially parallel x-rays. The beam stop 18 absorbs undiffracted and other radiation that has passed

through the mold walls 42a,b and sample section 30 within

a predetermined angular or spatial range. Tlie detector assembly 22 receives a first component 50 of the diffracted radiation associated with the crystalline phase and a second component 52 associated with the amorphous phase and

provides an output signal related to the first and second

components. The radiation source 10 can be any suitable x-ray, neutron,

or gamma source for producing radiation having energy

levels sufBcient to penetrate the mold walls 41a,b, sample

section 30, and any other intervening structure and a sufBcient intensity to provide a diffraction pattern from the sample section 30 at the detector assembly 22 that is distinguishable from other incident radiation, such as nondiffracted radiation not absorbed by beam stop 18, leakage from the radiation source 10, and radiation diffracted by

intervening structures, such as the mold walls 42a, 42b. More particularly, the energy level of radiation source 10

should be selected so that the collimated radiation 46 will travel through the first mold wall 42a, and a portion of the

144
5,589,690

sample section 30 so as lo pennil at least a portion of the radiation to undergo a coherent interaction with the crystalline phase 34 and/or amorphous phase. Further, the first and

second components of the diflfracted radiation (e.g., coherent

radiation) must then penetrate the remainder of the sample 5 section and the second mold wall 42b.

In selecting the energy of the radiation source 10, there is a tradeoff between achieving adequate transmission of the radiation through the mold walls 42a,b and other intervening

surfaces and the sample section 30 (the degree of transmis- 10 sion of radiation is greater at higher energies and lower at lower energies) and obtaining a sufiBciently large cross- section for the first and second components of the diffracted radiation (the probability of coherent interactions and therefore the quality of the diffraction image produced by the 15 detector assembly is higher at lower energies than higher

energies). At excessively high energies, Compton scattering of the radiation, which is substantially forward directed, can

be a problem.

In selecting the intensity of the radiation source, the 20 diffracted radiation received by the detector assembly 22

must have sufficient intensity to be separated from back- ground noise. Background noise is typically caused by

radiation diffracted by intervening structures, such as the mold, leakage radiation from the radiation source, Compton 25 scatter from the sample and structures surrounding the sample (e.g., mold, furnace), and non-diffracted radiation

that is not fully absorbed by the beam stop 18. It is necessary

to select the radiation source intensity such that the intensity of the diffracted pattern exceeds the intensity of the back- 30 ground noise. In view of the foregoing, in selecting both the energy and

intensity of the radiation source 10, the thicknesses and

compositions of the sample section 30 and mold walls 42a,b and other intervening structures (e.g., furnace walls) can be 35 measured and otherwise accounted for. These properties are important for predicting losses in the structures. Relatedly, the total mass attenuation coefficients for the sample section 30, mold 42, and other intervening structures can be determined for a predetermined range of source

radiation energies utilizing known values. By way of example, RG. 2 sets forth partial and total mass attenuation

coefficients for nickel. As can be seen from FIG. 2, the mass

attenuation coefficients are a function of the soiu-ce radiation

45 energy. After determining the total mass attenuation coefficients

for the sample section 30, mold 42, and other intervening

structures and the coefficient for coherent interactions in the sample at different potential energies of the source radiation, and the densities of the sample section 30, mold 42, and

other intervening structures, a ratio between the intensity of

the coherent radiation that would emerge from the sample

section 30, mold 42 and other intervening structures present

(1(E)), and the intensity of the source radiation received by

the detector assembly 22 in the absence of the sample

section 30, mold 42, and other intervening structures (IO(E)) can be determined for each potential energy (E) under

consideration for the source radiation. In this regard, a model of the transmission of radiation through a material encased in a mold can be represented by the following

equation:

KE)=IO(E)exp(-MWt(E)pw Wl )NL(exp(-MSl(E)psL) -exp(-

ps()isl(E) L+MSrtE) dx))) exp(-jiwt(E)pwW2),

wherein for a given source intensity at the energy E:,

40

IO(E) is the intensity at the detector of the radiation beam,

with no sample or mold present;

1(E) is the intensity of coherent (e.g., Rayleigh) scatter radiation which emerges from the sample section enclosed by mold walls; pwt(E) is the total mass attenuation coefficient in the mold

material (cm^ /g); pw is the density of the mold material (g/cm^); Wl is the thickness of the first mold wall 42a (cm); W2 is the thickness of the second mold wall 42b (cm); L is the thickness of the sample section 30(cm);

NfL is a large integer (e.g., 1000) which partitions the sample length (L) into small segments (dx);

|ist(E) is the total mass attenuation coefficient in the sample section 30 (cm^/g); ps is the density of the sample section 30 (g/cm^);

|isr(E) is the mass attenuation coefficient for coherent

(e.g., Rayleigh) radiation scattering in the sample section 30 (cm /g). Additional intervening structures, such as a furnace wall, can be accounted for in the equation by adding exponential

functions based on the total mass attenuation coefficient of

the intervening structure material at energy E, the density of

the material, and the thickness of the material. A more

complex model could further include the spatial redistribution of radiation during diffraction. The various ratios of 1(E) to IO(E) can then be plotted as a function of the corresponding potential energies of the source radiation to identify the preferred mean energy of the source radiation. By way of example, FIG. 3 provides such

a plot based on an aluminum sample (25 mm thick) encased

in an aluminum oxide mold (with 6 mm thick walls). The

peak in the plotted curve shows that there is an optimal range of source radiation energies. The optimum energy yields the highest production of diffracted radiation which is able to penetrate through the mold walls 42a. b and sample section

30. Because the mean energy of an x-ray source is generally one-half to one-third of the rated x-ray lube voltage the source preferably uses a tube voltage that is about two to three times the preferred energy peak. The preferred intensity of the source radiation received by

the detector assembly 22 is based on a predetermined

minimum detectable radiation level for the particular detector assembly 22 used, the dynamic range of the detector assembly 22, and the ambient noise radiation levels at the detector assembly 22 during operation. As noted above, the

intensity of the diffracted radiation received by the detector assembly 22 must be sufficient to permit the diffracted radiation to be distinguished from the noise. As will be

appreciated then, the tube current in the radiation source 10

should be selected to achieve the desired intensity at detector assembly 22.

In this regard, the radiation source for diffraction spot imaging preferably is not a microfocus radiation source. In other words, the radiation source preferably has focal spot dimensions larger than about 0.1 mm. Microfocus radiation sources, though useful for thin samples and thin mold walls, have insufficient intensity to provide a detectable transmission diffraction pattern image for the thicknesses of the samples and mold walls normally encountered in casting processes. Microfocus radiation sources typically handle

only small electrical currents (e.g., less than about 1 mA)

which are often too low to produce the desired intensity of

the source radiation for rapid inspection. As noted, the collimator 14 collimates the divergent source radiation 26 to a small spatial size. Collimators for

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radiation sources generally are designed using several apertures (in radiation-attenuating material) placed along the source radiation beam path. The aperture dimensions of the collimator are a tradeoflF between maximizing the intensity of the radiation beam transmitted (larger aperture size) and 5 minimizing the size of the spatial resolution cell. For

example, a radiation beam diameter of 1 mm has been found

suitable for a radiation source-to-sample distance of 200 mm

(e.g., 0.29 degrees angular aperture). Instead of collimating

apertures, the collimator could be comprised of x-ray optic devices which restrict the radiation beam to the desired dimensions. The collimated radiation 46 contains a plurality of substantially parallel rays. The beam stop 18 is an object composed of a material capable of absorbing a substantial portion of the transmitted

(undiflfracted) source radiation. A common type of beam stop '^ 18 is composed of tungsten or lead. The detector assembly 22 may comprise an x-ray imager

or merely an energy- sensor, or a combination thereof. An

x-ray imager allows for recording/processing of the spatial location of diffracted radiation by measuring the intensity of 20 radiation over a two-dimensional area. An energy-sensitive

detector allows for the recording/processing of the diffracted radiation received across the source energy spectrum. FIGS. 4-5 illustrate the difiFerent diffraction patterns received at an x-ray imager for crystalline and amorphous 25 material phases. The x-ray imager shows diffracted radiation from a crystalline phase (e.g., the first diffraction component) as a few spots, and from an amorphous phase (e.g., the second component) as a diffuse ring pattern. Specifically, FIG. 4 has spots 54a representing the first component and a

^q

diffuse ring pattern 58a representing the second component.

FIG. 5 has less intense spots 54b from the first component

and a more intense difftise ring pattern SSb from the second component, indicating that the sample section examined in FIG. 4 has a greater volume of crystalline phase and a ,, smaller volume of amorphous phase than the sample section examined in FIG. 5. The x and y axes of FIGS. 4 and 5

reflect spatial coordinates of the diffracted radiation received by the imager. Referring to FIG. 6, the output of an energy sensitive ^

detector is depicted versus the energy of the source radiation

at two time intervals. More particularly, FIG. 6 plots the quantity of photons (or counts) interacting with the energy

detector during a given time period versus the energy of the photons (i.e., corresponding with the radiation source energy ^, spectrum). Peaks 64a, i correspond to the spots 54a, fc, respectively, of FIGS. 4-5. The height of the peaks corre- sponds to the first component and thus to the amount of

crystalline phase in the sample. Accordingly, curve 62

corresponds to a greater amount of crystalline phase in the jq sample than curve 66. The unique Laue diffraction pattern of crystalline phases

relative to amorphous phases is explained by the Bragg

equation. The spots represent diffracted radiation that is a

solution to the Bragg equation:

55

1.24n = nX = 2Jsin6

60 where,

n is an integer; E is the energy (keV) of the source radiation which is diffracted; X is the wavelength (nm) of the incident source radiation which is diffracted; 65 d is the lattice spacing (nm) in the crystal structure of the

crystalline phase.

6 is the angle between the lattice plane and the incident

radiation. For a given orientation of the crystalline phase, diffracted radiation that is a solution to the Bragg equation forms spots 54a,b on the diffraction pattern. In contrast, the disordering of the amorphous phase produces the diffuse ring pattern 58a, fc. A detector assembly 22 utilizing the x-ray imager has

different components from a detector assembly utilizing an

energy-sensitive detector. A detector assembly 22 utilizing an x-ray imager generally includes a scintillator, an image

intensifier, and a charge coupled device video imager A

detector assembly 22 utilizing an energy-sensitive detector includes the detector (which is preferably a cooled, intrinsic germanium detector with an integral FET preamplifier), a high voltage detector bias supply, a linear spectroscopy

amplifier, and a multichannel analyzer. The components of

the detector assembly preferably are optimized for high

sensitivity in the 40 to about 500 keV range with a high count rate (e.g., greater than about 100,000 counts/sec)

capability. Energy-sensitive detectors generally provide a higher sensitivity than the x-ray imager and thus require a lower intensity x-ray source. The monitoring system in FIG. 1 is set to accommodate

a transmission-type diffraction pattern. As will be appreciated, the system could also be arranged to accommodate a back reflection-type diffraction pattern in which the diffrac- tion pattern is received by a detector assembly located on the radiation source side of the sample, or to accommodate a glancing incidence-type diffraction pattern in which the

diffraction pattern is received by the detector assembly

located at the side of the sample. The transmission-type Laue diffraction pattern is preferred as the diffraction pat- terns produced by the other two configurations are produced

by diffracted radiation that may not have passed completely

through the sample. It is important for the pattern to be produced by radiation passing completely through the sample to accurately locate the interface between the crystalline and amorphous phases at all locations within the casting cross-section. Additionally, the transmission mode is necessary to assess the relative crystalline/amorphous phase

fractions along the radiation beam path. Referring again to FIG. 1, the operation of a casting process using the present invention will now be described. The description will be based upon the use of the invention

in the casting of single-crystal or directionally-solidified

parts. The casting process is commenced by placing the molten

material into the mold 42 which rests on a chilled surface

(not shown). The mold 42 is contained within an induction or resistance-heated furnace (not shown) and is slowly withdrawn from the furnace as crystallization progresses upwards from the chilled surface. Source radiation 26 is generated by the radiation source

10, restricted spatially by the collimator 14 and directed through the following: the mold wall 42a, a portion of the amorphous phase 38, the interface between the amorphous

and crystalline phases, and a portion of the crystalline phase

34. The source radiation interacts with the crystalline and amorphous phases in the sample section to produce dif- fracted radiation having the first component 50 associated with the crystalline phase and the second component 52

associated with the amorphous phase. At least a portion of the first and second components are received by the detector assembly 22 which provides an

output signal related to the received portion of one and

preferably each of the first and second components. The

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output signal is used to monitor the interface between the

crystalline and amorphous phases. The output signal can be used to estimate the position of

the interface in the mold and/or the degree of crystallization of the crystalline phase. To do this, the first component may 5 be compared to the second component at selected time

intervals. For example, at a first time interval the source

radiation may be scaimed vertically up and down the mold

to locate either (i) the interface between the portion of the sample that is entirely an amorphous phase and that which

has both amorphous and crystalline phases (e.g., the top of

the dendrites 36) and/or (ii) the interface between the portion of the sample that is entirely a crystalline phase and that which has both amorphous and crystalline phases (e.g., the base of the dendrites 36). At a second time interval, the above-noted interfaces are again located. The distance '^ between the interface at the first time interval and the

interface at the second time interval divided by the period between the first and second time intervals provides the rate of crystallization. The first and second components can also be measured for 20 a defined area of the sample during different time intervals

to estimate the rate of crystallization. For example, the first and second components are compared with one another

during a first time interval to determine a first degree of

crystallization of the crystalline phase and during a second 25 time interval to determine a second degree of crystallization of the crystalline phase. The comparison can be based on the

relative intensities or magnitudes of the first and second

components. The crystallization rate can be determined

based on the first and second degrees of crystallization and 30

the period between the time intervals. As will be appreciated, computed tomography can be

applied to data regarding the position and/or crystallization

rate to generate a two- or three-dimensional representation of the interface between the amorphous and crystalline 35 phases. Computed tomography using the first and second components of diffraction will yield tomography images

with higher contrast between crystalline and amorphous

phases than computed tomographic images based on exploit- ing the small density difiFerences between the crystalline and 40 amorphous phases. Such an image could be generated during discrete time intervals to more precisely control the

casting process or to verify casting-process models. Based on the position and/or crystallization rate, a monitor signal can be provided to control the casting process. The 45 monitor signal can be used to control selected parameters in the casting process, such as the temperature of the furnace

and/or the rate of withdrawal of the mold from the furnace

(e.g., the duration of the casting), and the like. The monitor

signal can be manually or automatically generated. To 50 automatically generate the monitor signal, the first and

second components or the interface position or crystalliza- tion rate can be compared against predetermined values corresponding to each time interval during which the measurements are taken. If the measurement exceeds a maxi- 55 mum predetermined value (e.g., the rate of crystallization is too fast) or is less than a minimum predetermined value

(e.g., the rate of crystallization is too slow), an appropriate monitor signal is generated to adjust the casting process. To form the desired diffraction patterns, the source radia- 60

lion should be collimated. Preferably, the intensity of the portion of the first component received by the detector assembly and the portion of the second component received by the detector assembly together is at least about 0.1% of

the intensity of the source radiation. 65 The monitor signal can be used to cause a portion of the mold to be healed to a second temperature greater than a first

temperature of the mold to remelt a portion of the crystalline phase. After the portion of the crystalline phase is remelted,

the portion of the mold can be cooled to a third temperature

less than the second temperature to recrysiallize the remelted

portion of the crystalline phase. It is believed thai the remelling and recrystallizaiion of the defective portions of

the crystalline phase is an effective solution to decrease the number of castings which must be discarded for crystalline defects. As will be appreciated, the present invention is not

necessarily limited to casting processes but can be used in any process to monitor the position of the interface between

a crystalline phase and an amorphous phase, such as a liquid, or any other process involving an interface between a

crystalline and another crystalline or an amorphous phase.

TTie present invention can thus be used to monitor solidifi- cation processes, such as the casting of metals and alloys, growth of semiconductor boules, chemical precipitation processes, such as those in which crystalline precipitates are formed at high temperatures in an amorphous phase. By way of example, the present invention can detect the formation of a second crystalline phase in a crystalline

structure. The second crystalline phase has a different crystal structure than the surrounding crystal. The formation of a second crystalline phase in a surrounding crystalline phase

is employed in the alloying of metals. The formation of the second crystalline phase would produce diffracted radiation

different from the diffracted radiation produced by the surrounding crystalline phase in the absence of the second

crystalline phase. The diffraction pattern of the second

crystalline phase can be isolated by taking into account the

diffraction pattern produced by the surrounding crystalline phase in the absence of the second crystalline phase.

Additionally, the present invention can be used to detect defects in the crystal structure of the crystalline phase during

casting. A material having multiple crystals will produce a

diffraction pattern distinct from a crystalline phase having

only one crystal. For example, a crystalline having multiple

crystals will produce more spots than a crystalline phase

having only one crystal. In the event that more than one

crystal is detected in a monocrystalline phase would enable

the casting process to be altered to remelt the portion of the material having more than one crystalline structure followed by resolidification of the crystalline phase. In this matter, the portion of the castings discarded for crystalline defects can be significantly reduced. EXPERIMENT 1 A small piece of direclionally-solidified turbine blade

alloy was polished to make the directional nature of the microstructure observable. Incident x-ray beam and film plane angles were adjusted to 45° to give an angle of 90° between the x-ray beam and imager. A definite x-ray dif- fraction pattern was obtained using a 50 kVp x-ray tube

voltage. The x-ray tube voltage was increased to 75 kVp,

then to 100 kVp and finally to 150 kVp. The diffraction pattern persisted, with a very noticeable increase in intensity. The Compton scattering background increased somewhat

with tube voltage increases. This experiment verifies that x-ray diffraction can be obtained with x-ray tube voltages (100 kVp and 150 kVp) which are substantially higher than

that used in conventional (40 kVp) Laue measurements. EXPERIMENT 2

Experiment 1 was repeated with a 6 mm-thick piece of mold material typically used for single-crystal turbine blade

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11 12

castings (a mixture of aluminum oxide, silicon oxide, and

zirconium oxide) in a position between the source radiation and the turbine-blade alloy specimen. At an x-ray tube

voltage of 150 kVp, many of the diffraction spots near the beam stop (small-angle diffraction) remained. The expert- 5 menl confirms the ability to perform transmission diffraction even through typical casting mold material.

EXPERIMENT 3

10 A series of heating, melting, and recrystallizalion experi- ments were conducted using x-rays to locate the advancing

and receding interface between the solidified metal and

molten metal. A 22-millimeter-diameter polycrystalline 99.999% aluminum rod was placed in a quartz tube in a 15 furnace. The rod was heated to (652° C.) (near the melting

point) and the changing transmission Laue diffraction pat- tern was observed. The specimen was then cooled and

sectioned for analysis. Another experiment was conducted in which the alumi- 20 num rod was melted and resolidified. Real-time x-ray dif- fraction was employed to follow the progression of the

interface between the solidified aluminum and the molten aluminum. The difference between the pattern generated by

the high-temperature solid aluminum and the pattern gen- 25 erated by the liquid aluminum was dramatic and unmistakable. The diffraction spots from the solid disappeared as a

diffuse ring formed when the aluminum was fully melted.

EXPERIMENT 4 30 A copper rod was placed in a quartz tube, with a triangular cross-section. The tube was then inserted into a gradient

furnace. A 1 millimeter diameter, collimated x-ray beam was

directed into the furnace, and a real-time x-ray imager was 35 placed on the opposite side of the furnace. A 6 millimeter

thick, 3 millimeter diameter tungsten disk was positioned in the center of the primary x-ray beam emerging from the furnace to act as a beam slop. X-rays diffracted from the copper sample in the furnace passed to the sides of the beam 40 stop and were imaged. The furnace was manipulated remotely to move it verti- cally and horizontally. The vertical movement was used to scan the x-ray beam and imager with respect to the liquid/ solid copper boundary that was established in the gradient 45 furnace. Horizontal movement across the wedge-shaped

copper specimen permitted interrogating different thick- nesses. The temperature of the furnace was raised to melt the copper and then lowered to solidify it. The warming and 50 cooling sequence was repeated several times. As in the aluminum melting experiments, the solid copper produced a

diffraction image with bright diffraction spots. When the melting temperature of copper was exceeded, the ordered

diffraction pattern disappeared and was replaced by a diffuse 55 ring of x-ray scattering from the molten copper This experi- ment validated the sensing method for locating a liquid/solid boundary in a metal sample with physical characteristics (atomic number and density) similar to that of nickel-based

alloys. 60

EXPERIMENT 5 A gallium sample was placed in a container capable of producing a temperature gradient. A temperature controller 65 was connected to the heater to produce a steady-state boundary between the solid gallium (at the lop because its

density is less than the liquid gallium) and the liquid gallium. The position of the probing x-ray beam was moved

into the solid or liquid by a remote positioning fixture. X-ray

diffraction images and radiographic images (by removing

the collimaiing apertures in the x-ray beam) were altemalively taken. The density variation between the solid and

liquid gallium is great enough to produce a discemable

difference in brightness in a radiographic image. The abihty

to independently determine by radiographic image the position of the liquid/solid boundary (brighter versus darker

regions of the radiograph) provided a means for validating

the spatial performance of the x-ray imager. When the x-ray imager sensor was positioned to probe

only the solid gallium, bright diffraction spots were

observed. In the liquid, the diffuse scattering ring was

observed. At intermediate locations between liquid and

solid, the diffuse ring and diffraction spots were present, but both with decreased intensity in rough ratio to their relative amounts. The radiographic images produced with the x-ray images validated that the x-ray imager could accurately

locale the position of the liquid/solid interface, and verified

that the spatial resolution of the diffraction sensor is approxi- mately the size of the source radiation beam at the sample.

EXPERIMENT 6 The x-ray imager was replaced by an energy-sensitive

detector (intrinsic germanium). The much higher efficiency of the detector, compared to the imager, required the replace- ment of the collimating apertures. The 1 -millimeter diameter

aperture, used in experiments with the x-ray imager, pro- duced too intense a diffracted beam for the germanium

detector. A 0.2 millimeter diameter aperture was used. A

source-sample distance of 250 millimeters and a sampledetector spacing of 180 millimeters was used for the experi- ments. The spectra were obtained with an x-ray tube potential of 160 kV and a tube current of 1 mA.

Spectral peaks at approximately 100 keV and 130 keV

were produced by x-ray diffraction spots in a solid gallium

sample. There were no discemable peaks in the 100-130 keV spectrum recorded when the x-ray diffraction pattern in a liquid gallium specimen was examined. Although the

intensity (x-rays per unit area per second) was higher for the

diffraction spots, the spots were highly localized. The spec- trum for the liquid specimen, in contrast, recorded more

counts overall in each energy interval although the peak

intensity was lower. While various embodiments of the present invention have

been described in detail, it is apparent that modifications and

adaptations of those embodiments will occur to those skilled in the art. However, it is to be expressly understood that such

modifications and adaptations are within the scope of the present invention, as set forth in the following claims. What is claimed is:

1. A method for monitoring an interface between a crystalline phase and an amorphous phase of a material within a container, comprising the steps of: directing source radiation through at least one wall of a container and into an interface between a portion of a

crystalline phase of a material and a portion of an amorphous phase of said material contained in said container to provide diffracted radiation having a first diffraction component with a first spatial radiation

distribution associated with said crystalline phase and a second diffraction component with a second spatial radiation distribution associated with said amorphous

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13 14

phase, said first and second spatial radiation distribu- tions being spatially distinct; receiving at least a portion of at least one of said first diffraction component and said second diifraction component of said diffracted radiation on a radiation sen- 5 sitive detector means located outside of said container

to provide an output signal, said output signal including information corresponding to said spatial radiation dis- tribution of the received portion; and

using said output signal to monitor said interface between lo said crystalline phase and said amorphous phase.

2. The method as, claimed in claim 1, wherein:

said amorphous phase is a liquid phase of said material.

3. Tlie method as claimed in claim 2, wherein said materia] has a variable rate of crystallization, and said using 15 step comprises:

comparing during a first time interval a first output signal component corresponding with said first diffraction component with a second output signal component

corresponding with said second diffraction component 20

to provide a first compared value; comparing during a second time interval said first output

signal component with said second output signal component to provide a second compared value; and employing said first and second compared values to 25 determine said rate of crystallization between said first and second time intervals.

4. Tlie method as claimed in claim 1, wherein said receiving step comprises:

receiving both said first diffraction component and said 30 second diffraction component on said radiation sensitive detector means.

5. TTie method as claimed in claim 4, wherein said container is a casting mold.

6. The method as claimed in claim 1, wherein said 35 directing step comprises:

varying the intensities of said first and second diffraction components over time by changing the spatial location of said source radiation in a defined volume of said material. '^

7. T^e method as claimed in claim 1, wherein said receiving step comprises:

generating for successive time intervals corresponding

successive values relating to at least one of a first output

signal component corresponding with said first diffrac- tion component and a second output signal component

corresponding with said second diffraction component.

8. The method as claimed in claim 7, wherein said using

step comprises:

comparing said successive values with a predetermined

completion value that corresponds with a degree of

crystallization completion.

9. The method as claimed in claim 7, wherein said using

step comprises:

employing said successive values to determine a rate of

crystallization. 10. The method as claimed in claim 9, wherein said using

step comprises:

comparing said rate of crystallization to a predetermined 60 value.

11. The method as claimed in claim 7, wherein said successive values corresponding to said first output signal component and said successive values increase in magnitude

over said successive time intervals. 65 12. The method as claimed in claim 7, wherein said successive values corresponding to said second output signal

45

50

component and said successive values decrease in magnitude over said successive time intervals. 13. The method as claimed in claim 7, wherein:

said first and second output signal components corre- spond to the intensity of said first and second diffrac- tion components, respectively.

14. The method as claimed in claim 1, wherein said source

radiation is passed through a defined region of said container and said using step comprises:

comparing a first output signal component corresponding

with said first diffraction component with a second

output signal component corresponding with said sec- ond diffraction component to determine the portion of

said defined region occupied by at least one of said

crystalline phase and said amorphous phase.

15. The method as claimed in claim 1, wherein said using

step comprises:

comparing during a first time interval a first output signal component corresponding with said first diffraction component and a second output signal component

corresponding with said second diffraction component

to locate said interface at a first position; comparing during a second time interval said first and

second output signal components to locate said inter- face at a second position; and employing said first and second positions to determine a monitor signal. 16. The method as claimed in claim IS, wherein said first and second output signal components correspond to a time

interval and said using step comprises:

comparing said output signal to a predetermined completion value.

17. The method as claimed in claim 1, wherein said receiving step comprises:

comparing said first and second spatial radiation distri- butions to provide said output signal. 18. The method as claimed in claim 17, wherein said using step comprises:

using said monitor signal to establish at least one casting process control parameter.

19. TTie method as claimed in claim 17, wherein said using step comprises:

using said monitor signal to control in real time at least one casting process control parameter

20. The method as claimed in claim 17, further comprising:using said monitor signal to control at least one of the following parameters: the temperature of a furnace

containing said crystalline and amorphous phases and

the rate of withdrawal of said crystalline phase from

said furnace.

21. The method as claimed in claim 1, wherein a portion of said container is at a first temperature and further comprising: heating in response to said output signal said portion of

said container to a second temperature greater than said

first temperature to remelt a portion of said crystalline phase.

22. The method as claimed in claim 21, further comprising:cooling in response to said output signal said portion of

said container to a third temperature less than said second temperature to recrystallize said remelted portion of said crystalline phase.

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23. The method as claimed in claim 1, wherein:

said source radiation and the radiation sensitive detector means are positioned on opposing sides of said material

to produce transmission-type diffraction in said first and second diffraction components.

24. TTie method as claimed in claim 1, wherein said material crystallizes in a substantially vertical direction and

wherein:

said directing step comprises:

moving the source radiation relative to the container in a substantially vertical direction to monitor the pro- gression of the interface over time.

16

25. The method as claimed in claim 1, further comprising:

using at least one of a first output signal component

corresponding with said first diffraction component and

a second output signal component corresponding with

said second diffraction component to perform computed tomography and generate a two- or three- dimensional representation of the interface between the crystalline and amorphous phases.

150

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official source of information in the Federal Government regarding standards issued by NIST pursuant to the Federal Property and Administrative Services Act of 1949 as amended. Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717 (38 FR 12315, dated May 11, 1973) and Part 6 of

Title 15 CFR (Code of Federal Regulations).

NIST Interagency Reports (NISTIR)—A special series of interim or final reports on work performed by

NIST for outside sponsors (both government and non-government). In general, initial distribution is handled by the sponsor; public distribution is by the National Technical Information Service, Springfield,

VA 22161, in paper copy or microfiche form.
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