ASNT NDT Handbook Volume 4 Infrared and Thermal Testing

explorer La Salle’s final expedition, sank FIGURE 26. Radiography of submarine Hunley: (a) positioning
in 1886 along the coast of Texas and was a radioscopic image plate on hull exterior; (b) computed
discovered in 1995. Conservators have radiograph of hull’s rivets (the vessel was riveted from the
used radiographic testing to examine inside and sanded to improve its hydrodynamics); (c) setting
thousands of corroded objects, to identify up exposure of iridium-192.91
them and decide how they can be (a)
restored. For a variety of speeds both
medical and industrial film was used. (b)
Each artifact was radiographed three times
to provide images from different
angles.89,90

Hunley. The submarine H.L. Hunley served
the Confederacy in the American Civil
War, sinking the Union warship
Houstatonic in Charleston Harbor, South
Carolina, in 1964. The Hunley sank while
returning from that mission. Its wreck was
discovered in 1995 and salvaged with the
help of radiographic testing (Fig. 26).
When new, the submarine weighed
6800 kg (15000 lbm) and was 12 m (39 ft)
long.

The salvaged vessel was full of
sediment. A primary goal of the
radiographic testing was to measure the
width of the submarine’s plates and find
the seam line to help decide the best
point of entry. Confronted with the need
to create an image through 1.2 m (46 in.)
of sand and silt, the radiographers used
2.5 h exposures with a cobalt-60 source.
Digital images were manipulated to make
particular features more visible. Using this
information, conservators removed several
of the hull’s plates and excavated the
sediment inside the hull carefully, much
as an archeologist excavates a site on dry
land.

As with the Belle, corroded objects that
were discovered were then radiographed
to identify them and determine how best
to restore them. Recovered objects, in
addition to human bones, included
canteens, buttons, a thimble and a
lantern.91

Liberty Bell78,92,93 (c)

The Liberty Bell in Philadelphia rang to
celebrate the United States’ independence
in 1776. Gamma radiography was
performed with film in 1975 to assess the
bell’s integrity before a planned move
from Independence Hall to a different
building across the street (Fig. 27). The
radiographic testing used took place in
two phases: (1) a series of small sections
and (2) one large image of the entire bell.

The small radiographs were made with
standard 0.36 × 0.43 m (14 × 17 in.) film
exposed to a 1.9 TBq (52 Ci) iridium-192
source. Because of thickness variations in
the bell, exposure times ranged from
1.75 min at 1.9 TBq (52 Ci) to 17 min at
3.7 TBq (100 Ci).

The full size radiograph was made with
a vinyl covered package containing

Other Applications of Radiographic Testing 597

14 sheets of 1.3 × 2.1 m (52 × 84 in.) film. ball was positioned at a distance of 15 m
The sheets were made by slicing 2.1 m (50 ft) from the film.
(7 ft) sections from rolls of film in a width
of 1.3 m (52 in.), the width in which they The bell was radiographically tested
are manufactured before being cut to with film again in 2001 and the images
normal size. A 25 TBq (670 Ci) gamma ray have been compared with those from
projector containing cobalt-60 in a 900 kg 1975 to check for crack propagation and
(2000 lbm), 0.6 m (24 in.) diameter lead other changes.94

FIGURE 27. Gamma radiography of Liberty Marble Statues
Bell in 1976: (a) setup showing lead ball
containing cobalt-60; (b) film image.92 Caligula95
(a)
In the 1980s, the Virginia Museum of Fine
(b) Arts, Richmond, acquired a statue of the
Roman Emperor Caligula dating from the
first century of the Christian Era. A
fracture had separated the head from the
shoulders of the statue and a conservator
in 1970 had reconnected them using a
metal pin and glue. Radiography was
undertaken to determine the extent of the
1970 conservation efforts and, by
examination of the marble grain, to verify
that the head was originally part of the
rest of the statue. One of only two
complete statues of that emperor, the
statue is worth more if the head is
original. The radiographic tests helped
further studies to verify the head’s
authenticity (Fig. 28).

An iridium-192 source of 3.3 to 37 TBq
(90 to 1000 Ci) was placed 1.2 m (48 in.)
from the film cassettes taped to the head.
It required a series of 4 h exposures to get
images through 0.20 m (8 in.) of marble.

Pietà96

At the New York World’s Fair, in 1964, the
Vatican exhibited Michelangelo
Buonarroti’s Pietà. Before moving the
statue to the United States, the Vatican
commissioned a radiographer from the
United States to document its condition.
(Fig. 29a) The technician practiced by
radiographing stacks of marble window
sills but the Carera marble chosen by
Michelangelo proved harder and more
absorbing than the samples.

Radiographic work in the Basilica was
timed to avoid interference with Lenten
services. Film radiographs were made in
the day with a portable X-ray machine
operating up to 200 kV peak and exposure
times ranging from 30 s to 10 min.
Additional exposures were made
overnight with gamma equipment, using
a cobalt-60 source for the thickest parts of
the statue.

Fragile parts were of concern. The
statue had been moved in the past but
there was no record about the moves or of
damage to the statue. Radiographs of the
outstretched left hand of Mary revealed
that the fingers had been broken and
repaired using interior pins (Fig. 29b).

598 Radiographic Testing

FIGURE 28. Statue of Caligula: (a) placement Shipping experts used this information for
of film casette; (b) digitized film image.95 packing the statue.

(a) Paintings97

The scientific examination of art can be
divided into two basic categories:
destructive and nondestructive. Among
the destructive methods are those that
involve sampling, taking a small slice or
scraping for closer scrutiny, perhaps by
microscopy or spectroscopy. A
conservator’s goal, however, is carefully to
maintain valuable works of art and to
slow the inevitable deterioration.
Nondestructive testing is an invaluable
tool to this end. The art historian also
finds nondestructive testing an important
asset in the pursuit of information of
historical value — for example, about
creative techniques of a particular artist or
a certain period of art.

FIGURE 29. Michelangelo Buonarroti’s Pietà,
Saint Peter’s Basilica, Vatican: (a) film casette
placement; (b) image of hand, showing pins
used to repair broken fingers.96

(a)

(b)
(b)

Other Applications of Radiographic Testing 599

As part of the creative evolution of a 3. The original canvas of Rubens’ The
painting, an artist will often reconsider Virgin and Child Enthroned with Saints
during composition and paint over the (1628), Royal Museum of Fine Arts,
original idea. The artist may even paint Antwerp, had deteriorated and been
over an earlier works simply because the mounted on a second canvas, so
artist considers the earlier painting less radiography is the only way to
important than the need for another examine the original canvas.
canvas. A change can also be made by Radiographic testing has revealed few
someone other than the original artist. corrections to the original, suggesting
From the art historian’s point of view, a high level of mastery.
these underpaintings can afford insight
into artistic development or the 4. The Oyster Eater (1882), Royal Museum
techniques used to achieve a particular of Fine Arts, Antwerp, is a work from
effect. They can also help determine the James Ensor’s youth. It uses less
artist or the authenticity of a painting. opaque commercial oils from tubes.
Radiographic testing has revealed that
Three nondestructive methods derived Ensor mixed paints on the canvas
from the electromagnetic spectrum are more than on the palette.
used in the testing of two-dimensional
art: (1) ultraviolet fluorescent Vermeer97
photography, for study of chemistry on
the surface; (2) infrared reflectography Infrared reflectography and X-radiography
and thermography, sensitive to relatively have been applied in relating the painting
emissive hues near the surface; and techniques of seventeenth century
(3) X-radiography, suited for revealing Flemish artist Jan Vermeer to his
subsurface layers. X-radiography records distinctive style.106,107 View of Delft,
the distribution of pigments that have a known for the realistic impression it gives,
high absorption coefficient for X-rays. The was examined by Wheelock. The painting
X-rays used in X-radiography will is a cityscape of the seventeenth century
completely penetrate a canvas. However, mirrored in the still waters of a harbor.
if pigments such as white lead or Using infrared and X-radiography,
vermillion with high absorption conservators were able to determine the
coefficients are present,98 their changes made in the length and
distribution will be indicated on a positioning of the reflections in the water
photographic plate placed behind the and in the outlining of the city’s profile:
canvas. changes that Vermeer made to achieve his
realistic effect.
X-radiography has been used to
examine paintings since early in the In addition to learning more about
twentieth century.23 By revealing hidden Vermeer’s working techniques,
layers of a painting, the method can conservators attempted to determine
provide valuable information about compositional changes and also to learn
artistic techniques and materials. This more of actual physical condition — that
information can help conservators is, abrasion, restorations or any sort of
preserve or restore paintings.99-103 size alteration. Some changes to a
painting can result in questions of
Flemish Art104,105 authenticity, especially when they appear
to be done by someone other than the
Film radiography has been used for the original artist.106,107
examination and restoration of several
masterpieces of Flemish art. Baum97

1. Van Eyck’s Altarpiece of the Mystic Lamb Some of the examination procedures used
(1432), Saint Bavo’s Cathedral, Ghent, in the Intermuseum Conservation
consists of seven paintings on three Association laboratory are illustrated by
oaken boards. Radiographic testing has the infrared photographs of Charles
shown where apertures in the wood Baum’s Boy with Still Life, owned by the
grain had been filled with pigment Butler Institute of American Art. Fig. 30a
and mounting glue and revealed shows the portrait using normal light. No
several layers in the painting process. images other than that of the title are
apparent. An infrared photograph of the
2. Peter Paul Rubens’ Portrait of Gaspard same painting shows the sketch, or
Gevartius (1628), Royal Museum of underdrawing, for the face of the young
Fine Arts, Antwerp, was painted on a boy and the faint image of a young
panel consisting of five boards joined woman slightly above and to the right.
by dowel pins. Radiographic testing Figure 30b, the result of X-radiography, is
has revealed various details of Rubens’ a third image and appears to be that of an
technique. For example, a thick layer older man. In addition, darker areas
of paint confirmed a technique called slightly below center and lower left
“wet in wet” (alla prima). indicate some restoration.

600 Radiographic Testing

Higgens97 and infrared reflectography. The painting
appears as a depopulated landscape but,
The painting Randall’s Mill (1922-23), by when it is viewed with infrared
American artist Victor Higgens, was reflectography, the structure of a mill
examined by the Intermuseum appears, along with carriages filled with
Conservation Association laboratory figures, horsedrawn wagons and the figure
(Fig. 31a).107 The painting was still on the of a saddled donkey being led by a man.
original canvas stretcher and in a frame Photographic images of the infrared
with a brass label, which reads: “VICTOR reflectography examination were made
HIGGENS NA [sic] / 1884-1949 / from the black and white monitor as the
RANDALL’S MILL.” camera scanned various portions of the
canvas. With X-radiography, the structure
In light from a window, the raised of the mill is the dominant element of
surface of another painting appeared on Fig. 31b.
the canvas. After examining Randall’s Mill
under a raking light, the laboratory A painting of this description by
conservators assayed the oil painting with Higgens was detailed in the Indianapolis
various methods including X-radiography Star in 1924 but the painting
subsequently disappeared. In an interview
FIGURE 30. Charles Baum’s Boy with Still Life, in 1975, Helen Spiess Ferris, daughter of
previously attributed to Severin Roesen: Benjamin G. Randall, related the tale
(a) visible light photograph; explaining the painting beneath a
(b) X-radiograph of entire canvas showing
image apparently of older man.97 FIGURE 31. Victor Higgens’ Randall’s Mill: (a) visible light
photograph; (b) X-radiograph showing mill of title.97
(a)
(a)

(b)
(b)

Other Applications of Radiographic Testing 601

painting. Randall had built the mill of the
title. In the vicinity of the mill, he owned
a cabin that he made available to the
artist Higgens. Higgens painted the
picture of Randall’s Mill from that cabin.
On seeing the picture, Randall
pronounced it “the worst picture Higgens
ever painted.” The statement must have
bothered Higgens for some time, for the
overpainting is in a style that Higgens
used much later during the 1940s.

Closing

The applications in this chapter illustrate
the versatility of radiographic testing.

602 Radiographic Testing

References

1. Snow, S.G. and R.A. Morris. 10. Whittaker, J.W. and S.G. Snow.
“Radiation Gaging.” Nondestructive “A Radiation Attenuation Technique
Testing Handbook, second edition: for Simultaneous Determination of
Vol. 3, Radiography and Radiation Layer Thickness in a Bi-Layered
Testing. Chapter 16. Columbus, OH: Structure.” Materials Evaluation.
American Society for Nondestructive Vol. 34, No. 10. Columbus, OH:
Testing (1985): p 674-704. American Society for Nondestructive
Testing (October 1976): p 224-229.
2. Davis, R.S. “Early Development of
Process Automation with Nucleonic 11. Reynolds, G.M. “Neutron Gaging
Measurement Gages.” Materials Systems.” Practical Applications of
Evaluation. Vol. 47, No. 10. Neutron Radiography and Gauging.
Columbus, OH: American Society Special Technical Publication 586.
for Nondestructive Testing ASTM International (1976): p 58.
(October 1989): p 1190-1191.
12. Knoll, G.F. Radiation Detection and
3. Trout, E.D., R.M. Gager and Measurement, third edition. New
A.L. Pace. “Possible Industrial York: John Wiley and Sons (2000).
Applications of Soft X-Radiation
15 to 100 Kilovolts.” Nondestructive 13. Koicki, S., A. Koicki and V. Aydacic.
Testing. Vol. 7, No. 3. Columbus, Nuclear Instrumentation and Methods
OH: American Society for (1973): p 297.
Nondestructive Testing
(Winter 1948-1949): p 20-24. 14. Davis, R.S. “Nondestructive Gaging
with Radiation Sources.” Materials
4. Reider, J.E. “Industrial Nucleonic Evaluation. Vol. 47, No. 9.
Gaging.” Nondestructive Testing. Columbus, OH: American Society
Vol. 15, No. 6. Columbus, OH: for Nondestructive Testing
American Society for Nondestructive (September 1989): p 1054, 1056,
Testing (November-December 1957): 1058, 1060.
p 360-365.
15. Baird, D.L. “Using 3D X-Ray
5. Clayton, J.D. “Thickness Gaging by Inspection for Process
Gamma Ray Attenuation.” Materials Improvements.” Proceedings of
Evaluation. Vol. 31, No. 2. NEPCON West Conference. Des
Columbus, OH: American Society Plaines, IL: Cahners Publishing
for Nondestructive Testing (1993).
(February 1973): p 27-32.
16. Sack, T. “Implementation Strategy
6. Ball, E. “A Method for Non-Contact for an Automated X-Ray Inspection
Thickness and Conductivity Machine.” Proceedings of Nepcon West
Gaging.” Materials Evaluation. Conference. Des Plaines, IL: Cahners
Vol. 33, No. 9. Columbus, OH: Publishing (1991).
American Society for Nondestructive
Testing (September 1975): p 54A, 17. Olsen, R. “More Than Just a Pretty
57A. Picture: Real-Time X-Ray Image
Enhancement in the Electronics
7. Coulter, J.E. X-Ray Fluorescence Industry.” Materials Evaluation.
Technique for Measuring Coating Vol. 46, No. 11. Columbus, OH:
Thickness. Y-1927. Oak Ridge, TN: American Society for Nondestructive
Oak Ridge Y-12 Plant (1974). Testing (October 1988):
p 1403-1408.
8. White, J.D. Compton Scattering
Technique for Measuring the Area 18. Silva, F. “Automated X-Ray
Density of Glass-Reinforced Structures. Inspection Strategies.” Real-Time
Y-1714. Oak Ridge, TN: Oak Ridge Radioscopy and Digital Imaging
Y-12 Plant (1970). [Mashantucket, CT, August 1998].
Columbus, OH: American Society
9. Foukes, R.A., J.S. Watt, for Nondestructive Testing (1998):
B.W. Seatonberry, A. Davison, appendix.
R.A. Greig, H.W.G. Lowe and
A.C. Abbott. International Journal of
Applied Radiation and Isotopes.
Vol. 29, No. 12 (1978): p 721.

Other Applications of Radiographic Testing 603

19. Buechler, D.W. “Real-Time 29. “Mobile X-Ray Unit (on a Trailer)
Radiography for Electronics ‘Eyes’ Airport Luggage, Packages.”
Reliability Assessment.” Materials Materials Evaluation. Vol. 30, No. 5.
Evaluation. Vol. 45, No. 11. Columbus, OH: American Society
Columbus, OH: American Society for Nondestructive Testing
for Nondestructive Testing (May 1972): p 54A.
(November 1987): p 1326-1329.
30. Battema, J.P. “Nondestructive
20. Marchese, M. and K.A. Glodowski. Testing Fights Terrorism.” Materials
“Real-Time Microfocus Radiography Evaluation. Vol. 44, No. 11.
for Electronic Failure Analysis.” Columbus, OH: American Society
Materials Evaluation. Vol. 49, No. 12. for Nondestructive Testing (October
Columbus, OH: American Society 1986): p 1304, 1310, 1314, 1316.
for Nondestructive Testing
(December 1991): p 1481-1485. 31. Tsacoumis, T.P., ed. Access Security
Screening: Challenges and Solutions.
21. “X-Ray Technology Digital Detector Special Technical Publication 1127.
Based Systems.” Technical note. West Conshohocken, PA: ASTM
Bohemia, NY: V.J. Technologies International (1992).
(2000).
32. Lanza, R.C. “Visualization and
22. Tollner, E. and M. Shahin. “X-Ray Imaging.” Aviation Security Problems
Imaging for Classifying Food and Related Technologies. SPIE
Products Based on Internal Defects.” Proceedings, Vol. CR42. Bellingham,
ASNT Spring Conference and 9th WA: International Society for
Annual Research Symposium Abstracts Optical Engineering (1992):
[Birmingham, AL]. Columbus, OH: p 104-125.
American Society for Nondestructive
Testing (March 2000): p 89-90. 33. Verbinski, V.V., J. Payne and
M. Snell. “Recent Developments in
23. St. John, A. and H.R. Isenburger. the VACIS Gamma Radiography
Industrial Radiography. New York, NY: Systems.” Enforcement and Security
John Wiley and Sons (1934). Technologies. SPIE Proceedings,
Vol. 3575. Bellingham, WA:
24. Schmitt, P. “Lebensmittelscanner.” International Society for Optical
Arbeitskreis Industrielle Engineering (1998): p 368-374.
Röntgenprüfverfahren. Ausgabe 1
[ZfP-Zeitung, Ausgabe 79]. Berlin, 34. De Moulpied, D.S., P.J. Rothschild
Germany: Deutsche Gesellschaft für and G.J. Smith. “X-Ray BodySearch
Zerstörungsfreie Prüfung Eliminates Strip Search in Montana
(April 2002): p 4. Prison.” Enforcement and Security
Technologies. SPIE Proceedings,
25. Katz, R., M.R. Lee and M. Milner. Vol. 3575. Bellingham, WA:
“X-Ray Inspection of Wheat.” International Society for Optical
Nondestructive Testing. Vol. 9, No. 2. Engineering (1998): p p 175-181.
Columbus, OH: American Society
for Nondestructive Testing 35. Bell, C.J. “Nuclear Technologies for
(Fall 1950): p 16-18. Explosives Detection.” Aviation
Security Problem and Related
26. Vozzo, J.A. “Seed Radiography.” Technologies. SPIE Proceedings,
Materials Evaluation. Vol. 46, No. 11. Vol. CR42. Bellingham, WA:
Columbus, OH: American Society International Society for Optical
for Nondestructive Testing Engineering (1992): p 137-166.
(October 1988): p 1450, 1452-1455.
36. Hussein, E.M. “Detection of
27. Beaton, J.A., W.B. White and Explosive Materials Using Nuclear
F.H. Berry. “Radiography of Trees Radiation: A Critical Review.”
and Wood Products.” Materials Aviation Security Problem and Related
Evaluation. Vol. 30, No. 10. Technologies. SPIE Proceedings,
Columbus, OH: American Society Vol. CR42. Bellingham, WA:
for Nondestructive Testing International Society for Optical
(October 1972): p 14A-17A. Engineering (1992): p 126-136.

28. Brenizer, J.S., K.W. Tobin, 37. Fishbein, R.H. “Pulsed Fast Neutron
J.M. Hylko, D.D. McRae and Analysis May Help Quench
R.W. Jenkins, Jr. “Quantitative Terrorism.” Materials Evaluation.
Measurement of Equivalent Water Vol. 55, No. 12. Columbus, OH:
Density in a Burning Cigarette.” American Society for Nondestructive
Materials Evaluation. Vol. 45, No. 11. Testing (December 1997): p 1330,
Columbus, OH: American Society 1332, 1334.
for Nondestructive Testing
(November 1987): p 1310-1314.

604 Radiographic Testing

38. Baltzer, K.R. “Is There a Role for 46. Sakine, I. and M. Fujinawa.
Nondestructive Testing in “Exploratory Tests of Corrosion of
Preventing Terrorism and Increasing Reinforcing Steel in Concrete by
Homeland Security?” Materials X-Radiography.” Materials
Evaluation. Vol. 60, No. 4. Evaluation. Vol. 42, No. 1.
Columbus, OH: American Society Columbus, OH: American Society
for Nondestructive Testing for Nondestructive Testing
(April 2002): p 513-517. (January 1984): p 121-126.

39. Marr, W.A. and C. Fairhurst, eds. 47. Forbis, J.E. “Radiography for
Nondestructive and Automated Testing Building Renovation.” Materials
for Soil and Rock. Special Technical Evaluation. Vol. 59, No. 6.
Publication 1350. West Columbus, OH: American Society
Conshohocken, PA: ASTM for Nondestructive Testing
International (1999). (June 2002): p 685-686, 688,
690, 692-694.
40. Bernhard, R.K. and M. Chasek. “Soil
Density Determination by Means of 48. Saleh, H.H., G. Washer and
Radioactive Isotopes.” Nondestructive M. Moore. “The Use of X-Ray
Testing. Vol. 11, No. 8. Columbus, Computed Tomography for
OH: American Society for Highway Applications.” ASNT Fall
Nondestructive Testing Conference and Quality Testing Show
(November-December 1953): 2000 Paper Summaries Book
p 17-23. Errata, Vol. 12, No. 1 [Indianapolis, IN]. Columbus, OH:
(January-February 1954): p 40. American Society for Nondestructive
Testing (November 2000): p 126.
41. Ritz, V.H. “Broad and Narrow Beam
Attenuation of Ir-192 Gamma Rays 49. Livingston, A. and H. Saleh.
in Concrete, Steel, and Lead.” “Development of an Epithermal
Nondestructive Testing. Vol. 16, No. 3. Neutron Detector for
Columbus, OH: American Society Nondestructive Measurement of
for Nondestructive Testing Concrete Hydration.” Nondestructive
(May-June 1958): p 269-272. Characterization of Materials VIII:
Proceedings of the Eighth International
42. Runkiewicz, L. “Application the Symposium held in Boulder, Colorado,
Radiographical Testing for Control June 15-20, 1997. New York, NY:
of Building Constructions of Plenum Press (1998): p 535-540.
Concrete in Poland.” 3rd European
Conference on Nondestructive Testing 50. Livingston, R.A. and H.H. Saleh.
[Florence, Italy]. Vol. 1. Brescia, “Specification and Design of a
Italy: Italian Society for Portable Prompt Gamma/Neutron
Non-Destructive Testing, for the Activation System for
European Societies for Nondestructive Determination of
Nondestructive Testing Chloride in Reinforced Concrete.”
(October 1984): p 142-153. Topics on Nondestructive Evaluation:
Vol. 2, Nondestructive Testing and
43. Mitchell, T.M. “Radioactive/Nuclear Evaluation of Infrastructure.
Methods.” CRC Handbook on Columbus, OH: American Society
Nondestructive Testing of Concrete. for Nondestructive Testing (1998):
Boca Raton, LA: CRC Press (1990): p 83-96.
p 227-252.
51. Saleh, H.H. and R.A. Livingston.
44. Clarke, E.T. “Cobalt-60 Radiography “Experimental Evaluation of a
of Concrete.” Materials Evaluation. Portable Neutron-Based
Vol. 47, No. 10. Columbus, OH: Gamma-Spectroscopy System for
American Society for Nondestructive Chloride Measurements in
Testing (October 1989): Reinforced Concrete.” Journal of
p 1200-1203. Radioanalytical and Nuclear
Chemistry. Vol. 244, No. 2.
45. Niehous, F., G. Coen, R. Kretschmer Lausanne, Switzerland: Elsevier
and M. Biercher. “Radiographic Sequoia (May 2000): p 367-371.
Inspection of Prestressed Concrete
up to 1600 mm Wall Thickness 52. Livingston, R.A., H.H. Saleh,
Using a 9 MeV Linear Accelerator.” R.C. Block and P.J. Brand. “Time of
11th World Conference on Flight Calibration of Li-6 Glass
Nondestructive Testing [Las Vegas, Epithermal Neutron Detectors.”
Nevada]. Vol. 1. Columbus, OH: Applied Radiation and Isotopes.
American Society for Nondestructive Vol. 53, No. 4-5. Oxford, United
Testing (November 1985): Kingdom: Pergamon Press
p 528-534. (May-June 2000): p 773-777.

Other Applications of Radiographic Testing 605

53. Hellier, C. “Who Will Inspect Our 62. Yang, J. “X-Ray Radiography Applied
Bridges?” Materials Evaluation. to the Study of the Ancient
Vol. 41, No. 12. Columbus, OH: Manufacturing Technique and the
American Society for Nondestructive State of Conservation of Cultural
Testing (November 1983): Relics.” 15th World Conference on
p 1352-1355. Non-Destructive Testing [Rome, Italy].
Brescia, Italy: Italian Society for
54. Thomas, G., S. Benson, P. Durbin, Non-Destructive Testing Monitoring
N. Del Grande, J.J. Haskins, Diagnostics (October 2000): p 170.
A. Brown and D.J. Schneberk.
“Nondestructive Evaluation 63. Schiekel, M., G. Haase, A. Meister
Techniques for Enhanced Bridge and M. Seibitz. “Investigation of
Inspection.” Review of Progress in Historical Glasses Using Natural
Nondestructive Evaluation. Vol. 13B. Born Radioactivity.” 15th World
New York, NY: Plenum Press (1994): Conference on Non-Destructive Testing
p 2083-2090. [Rome, Italy]. Brescia, Italy: Italian
Society for Non-Destructive Testing
55. Newell, R.S. and P.J. Stolarski. “Use Monitoring Diagnostics
of a Portable Linear Accelerator to (October 2000): p 174.
Radiograph a Bridge Drainage
Pump.” Materials Evaluation. Vol. 50, 64. Alonso, M.A. M Arroyo, V. Gil,
No. 9. Columbus, OH: American E.M. de Salinas and G. Delojo.
Society for Nondestructive Testing “A Radiographic Study of Insect
(September 1992): p 1084, Attacks in Woods.” 7th European
1086-1087. Conference on Non-Destructive Testing
[Copenhagen, Denmark]. Vol. 1.
56. Bell, R.D. “Field Radiography — Copenhagen, Denmark: 7th ECNDT
Images from the Past.” Materials (May 1998): p 400-408.
Evaluation. Vol. 42, No. 7.
Columbus, OH: American Society 65. Mísˇek, B. and L. Ptácˇek. “Some Data
for Nondestructive Testing Obtained on X-Ray and
(June 1984): p 849-851. Neutronographic Examination of
Heat Resistant Ni-Base Alloys.” 3rd
57. “Radiography Saves Baseball European Conference on Nondestructive
Season.” Materials Evaluation. Testing [Florence, Italy]. Vol. 1.
Vol. 47, No. 10. Columbus, OH: Brescia, Italy: Italian Society for
American Society for Nondestructive Non-Destructive Testing, for the
Testing (October 1989): p 1162. See European Societies for
also Vol. 48, No. 4 (April 1990): Nondestructive Testing
p 504. (October 1984): p 246-251.

58. AWS D1.12, Structural Welding Code 66. Ptácˇ ková, M. and L. Ptácˇek.
— Steel. Section 8, “Buildings.” “Complex Examination of
Miami, FL: American Welding Corrosion Damage in Archaeological
Society (1986). Finds of Etruscan Bronze Jewels.”
3rd European Conference on
59. Reimers, P. and J. Riederer. Nondestructive Testing [Florence,
“Zerstörungsfreie Prüfung Italy]. Vol. 1. Brescia, Italy: Italian
Kulturgeschichtlicher Objekte durch Society for Non-Destructive Testing,
Computertomographie (CT).” 3rd for the European Societies for
European Conference on Nondestructive Nondestructive Testing
Testing [Florence, Italy]. Vol. 1. (October 1984): p 252-261.
Brescia, Italy: Italian Society for
Non-Destructive Testing, for the 67. Gottlieb, B. “NDT Examination of
European Societies for Bronze Lurs.” 7th European
Nondestructive Testing Conference on Non-Destructive Testing
(October 1984): p 305-313. [Copenhagen, Denmark]. Vol. 1.
Copenhagen, Denmark: 7th ECNDT
60. Boutaine, J.L. “Radiography Applied (May 1998): p 436-443.
to Non Destructive Examination of
Cultural Objects.” 7th European 68. Rossi, M. “High Resolution
Conference on Non-Destructive Testing 3D Computed Tomography of Small
[Copenhagen, Denmark]. Vol. 1. Archaeological Sculptures.”
Copenhagen, Denmark: 7th ECNDT 7th European Conference on
(May 1998): p 391. Non-Destructive Testing [Copenhagen,
Denmark]. Vol. 1. Copenhagen,
61. Lavayssiére, B. and N. Lacoudre. Denmark: 7th ECNDT (May 1998):
“Application of Radiography for the p 409-415.
Conservation and Restoration of
Archaeological Objects.” 7th
European Conference on
Non-Destructive Testing [Copenhagen,
Denmark]. Vol. 1. Copenhagen,
Denmark: 7th ECNDT (May 1998):
p 416-419.

606 Radiographic Testing

69. Tartari, A. “Compton Scattering 77. “The Statue of Liberty: The
Elemental Imaging of a Deep Layer Restoration in Retrospect.” Materials
Performed with the Principal Evaluation. Vol. 44, No. 8.
Component Analysis.” 15th World Columbus, OH: American Society
Conference on Non-Destructive Testing for Nondestructive Testing
[Rome, Italy]. Brescia, Italy: Italian (July 1986): p 891-895.
Society for Non-Destructive Testing
Monitoring Diagnostics 78. Berntson, C.M. “Nondestructive
(October 2000): p 158. Testing Sheds Light on Preserving
America’s Past.” Materials Evaluation.
70. Caneva, C. “XRF Spectrometers for Vol. 43, No. 10. Columbus, OH:
Non-Destructive Investigations in American Society for Nondestructive
Art and Archaeology.” 15th World Testing (September 1985):
Conference on Non-Destructive Testing p 1180-1182, 1184-1186.
[Rome, Italy]. Brescia, Italy: Italian
Society for Non-Destructive Testing 79. Hatziandreau, L. and G. Ladopoulos.
Monitoring Diagnostics “Use of Radiography for Solution of
(October 2000): p 171. Diagnostic Problems Existing in
Marble Monuments.”
71. Rossi, M., D. Romani and D. Picchi. Materialprüfung. Vol. 22. Berlin,
“Investigation of Small Egyptian Germany: Bundesanstalt für
Mummies by 3D Computed Materialforschung und Prüfung
Tomography.” 15th World Conference (July 1980): p 298-300.
on Non-Destructive Testing [Rome,
Italy]. Brescia, Italy: Italian Society 80. Clarke, E.T. “Radiography of Ancient
for Non-Destructive Testing Structures on the Acropolis of
Monitoring Diagnostics Athens.” Technology and
(October 2000): p 159. Conservation. Vol. 8, No. 3. Boston,
MA: Technology Organization
72. “NSWC X-Rays Mummified Bull.” (Fall 1983): p 18-22.
Materials Evaluation. Vol. 36, No. 5.
Columbus, OH: American Society 81. “Radiography Aids Renovation of
for Nondestructive Testing Capitol.” Materials Evaluation.
(April 1978): p 58. Vol. 43, No. 10. Columbus, OH:
American Society for Nondestructive
73. Lombardo, B., G. Conlogue and Testing (September 1985): p 1148,
R. Colten. “The Use of Computed 1150-1151.
Radiography to Survey Mummified
Remains.” ASNT Fall Conference and 82. Bonin, H.W. and C.J. Thorp.
Quality Testing Show 2000: Paper “Neutron Moisture Gage for Roofing
Summaries Book [Indianapolis, IN]. Surveys: Experiment and
Columbus, OH: American Society Simulation.” 3rd European Conference
for Nondestructive Testing on Nondestructive Testing [Florence,
(November 2000): p 127. Italy]. Vol. 1. Brescia, Italy: Brescia,
Italy: Italian Society for
74. Paderni, L. and M. Micheli. “X-Ray Non-Destructive Testing, for the
Study of Peruvian Funeral ‘Fardos’ of European Societies for
the Museo Preistorico Etnografico Nondestructive Testing
‘Luigi Pignorini.’“ 3rd European (October 1984): p 224-229.
Conference on Nondestructive Testing
[Florence, Italy]. Vol. 1. Brescia, 83. Blancato, R.J. “Radiography Finds
Italy: Italian Society, for ‘Broken Bones’ in Cape Hatteras
Non-Destructive Testing, for the Lighthouse.” Materials Evaluation.
European Societies for Vol. 38, No. 3. Columbus, OH:
Nondestructive Testing American Society for Nondestructive
(October 1984): p 263-275. Testing (March 1980): p 13-15.

75. Zangerl, R. “The Use of X-Rays in 84. Clarke, E.T. “Radiography of the
the Study of Fossils.” Nondestructive Cape Hatteras Lighthouse.”
Testing. Vol. 7, No. 1. Columbus, Technology and Conservation. Vol. 5,
OH: American Society for No. 1. Boston, MA: Technology
Nondestructive Testing Organization (Spring 1980): p 20-24.
(Summer 1948): p 29-31.
85. Minato, S. “Feasibility of
76. “X Rays Provide Researcher with Cosmic-Ray Radiography: A Case
Views of Coral Growth Patterns.” Study of a Temple Gate as a
Materials Evaluation. Vol. 37, No. 9. Testpiece.” Materials Evaluation.
Columbus, OH: American Society Vol. 46, No. 11. Columbus, OH:
for Nondestructive Testing American Society for Nondestructive
(August 1979): p 26-27. Testing (October 1988):
p 1468-1470.

Other Applications of Radiographic Testing 607

86. Livingston, R.A. “Transferring 97. Humphries, H. “Infrared Testing in
Technology from Conservation Art Conservation.” Materials
Science to Infrastructure Renewal.” Evaluation. Vol. 45, No. 4.
Public Roads. Vol. 58, No. 1. McLean, Columbus, OH: American Society
VA: Federal Highway Administration for Nondestructive Testing
(Summer 1994). (April 1987): p 426-428, 430.

87. Alvarez, L.W. “Search for Hidden 98. Van Asperen de Boer, J.R.J. “Infrared
Chambers in the Pyramids.” Science. Reflectography: A Contribution to
Vol. 167. Washington, DC: the Examination of Earlier European
American Association for the Paintings.” Dissertation. Amsterdam,
Advancement of Science (1970): Netherlands: University of
p 832-839. Amsterdam (July 1970): p 11-15.

88. “Hellier Examines Historic Vessel 99. Graham, D. and T. Eddie. X-Ray
with Modern NDT Tests.” Materials Techniques in Art Galleries and
Evaluation. Vol. 36, No. 7. Museums. Boston: Adam Hilger
Columbus, OH: American Society Limited (1985).
for Nondestructive Testing
(June 1978): p 70-71. 100. Rossi, M., F. Casali, A. Bacchilega
and D. Romani. “An Experimental
89. Kleven, S. “Use of Computed X-Ray Digital Detector for
Radiology during the Archaeological Investigation of Paintings.”
Conservation of LaSalle’s Ship — 15th World Conference on Non-
The Belle.” 15th World Conference on Destructive Testing [Rome, Italy].
Non-Destructive Testing [Rome, Italy]. Brescia, Italy: Italian Society for
Brescia, Italy: Italian Society for Non-Destructive Testing Monitoring
Non-Destructive Testing Monitoring Diagnostics (October 2000): p 160.
Diagnostics (October 2000): p 157.
101. Pancyzk, E., M. Ligeza, K. Pytel,
90. “Uncovering Historical Treasures A. Kalicki, L. Ro~winska, B. Sartowska
Using NDT.” Materials Evaluation. and L. Walis. “Neutron-Induced
Vol. 57, No. 7. Columbus, OH: Autoradiography in the Study of Oil
American Society for Nondestructive Paintings by Tintoretto, Marieschi
Testing (July 1999): p 736. and Bellotto.” 15th World Conference
on Non-Destructive Testing [Rome,
91. Fanning, D.F. “The Confederate Italy]. Brescia, Italy: Italian Society
Submarine H.L. Hunley and for Non-Destructive Testing
Nondestructive Testing. Materials Monitoring Diagnostics (October
Evaluation. Columbus, OH: 2000): p 179.
American Society for Nondestructive
Testing (March 2002): p 409-413, 102. “The Mysterious Paintings of Francis
416-419. Picabia.” Worldwide. Vol. 7. Mortsel,
Belgium: Agfa-Gavaert NV [n.d.].
92. “How They Did It — Radiographing
the Liberty Bell.” Materials 103. “The Hermitage Museum
Evaluation. Vol. 34, No. 2. Conservation Project: Titian’s The
Columbus, OH: American Society Flight into Egypt.” Worldwide.
for Nondestructive Testing Vol. 8/9. Mortsel, Belgium:
(February 1976): p 14A-16A, Agfa-Gavaert NV [n.d.].
18A, 26A.
104. Flemish Masterpieces X-Rayed with
93. Clarke, E.T. “Radiographing the Structurix Industrial X-Ray Film. Press
Liberty Bell.” Foundry Trade Journal. release. Mortsel, Belgium:
Vol. 141. London, United Kingdom: Agfa-Gavaert NV [n.d.].
Institute of British Foundrymen
(August 1976): p 223-228. 105. The Ingenuity of Flemish Art and NDT
Technology Combined. Brochure.
94. “Examining the Liberty Bell.” The Mortsel, Belgium: Agfa-Gavaert NV
NDT Technician. Vol. 1, No. 3. [1988].
Columbus, OH: American Society
for Nondestructive Testing (July 106. Wheelock, Arthur K., Jr. “NEA
2002): p 1-5. Fellows’ Diary: Vermeer’s Painting
Technique.” Art Journal. Vol. 41,
95. “Radiography Aids Art Conservation No. 2. New York, NY: Hearst
of Caligula Statue.” Materials Corporation (Summer 1981):
Evaluation. Vol. 47, No. 10. p 162-164.
Columbus, OH: American Society
for Nondestructive Testing 106. Wheelock, A.K., Jr. Vermeer and the
(October 1989): p 1129-1131. Art of Painting. New Haven, CT: Yale
University Press (1995).
96. “George Corney’s Radiographs Help
Move Vatican’s Pieta.” Materials 107. Porter, D. Correspondence
Evaluation. Vol. 22, No. 6. (January 1987).
Columbus, OH: American Society
for Nondestructive Testing
(June 1964): p 279.

608 Radiographic Testing

22

CHAPTER

Attenuation Coefficients

Frank A. Iddings, San Antonio, Texas

PART 1. Introduction to Attenuation Coefficients

The attenuation of an X-ray or gamma ray where µM is the mass attenuation
beam passing through matter (and the coefficient and where ρ is the density of
beam’s resulting attenuation) is the the absorbing material. The linear
consequence of a series of single events. attenuation coefficient has a dimension
During each event a photon is removed of cm–1.
from the beam after interaction with a
nucleus or an orbital electron in the The linear attenuation coefficient µL of
attenuating material. The total probability water at 1 MeV, for example, is:
(per atom) for scattering or absorption of
a photon of the original energy is given 0.0705 cm2 ⋅ g–1
by a proportionality constant σ. This is
often referred to as the cross section × 1 g ⋅ cm–3 = 0.0705 cm–1
because it has the dimensions of an area.
Such cross sections are measured in a unit where 1 is the density ρ in gram per cubic
of 10–28 m2. In physics, this unit has been centimeter at standard temperature and
called barn (b), where 1 b = 100 fm2 = pressure and where 0.0705 is the mass
10–28 m2 = 10–24 cm2. attenuation coefficient µM for water.

The total attenuation coefficient is the The linear attenuation coefficient µL
sum of the attenuation coefficients due to for air at 0.020 MeV is:
compton scattering, the photoelectric
effect and pair production. The 0.761 × 0.0012 = 0.91 × 10–3 cm–1
photoelectric effect is that process in which
a photon transfers its total energy to an where 0.0012 is the density ρ of air in
electron in some shell of an atom. It is gram per cubic centimeter and 0.761 is its
most significant at lower photon energies. mass attenuation coefficient µM.
As photon energy increases, compton Calculation of the mass attenuation
scattering becomes the main process coefficients for air and water is shown
contributing to attenuation. Very high below).
energy photons are absorbed by pair
production, in which a photon is converted Mass Attenuation Coefficient
into an electron and a positron. This
process occurs in the electrical field of a The mass attenuation coefficient µM of a
nucleus and requires a minimum photon compound or mixture is the sum of the
energy of 1.02 MeV. mass attenuation coefficients of the
constituent elements, weighted in
The total attenuation coefficient can be proportion to their relative abundance R.
expressed in three different forms:
( ) ( )(2) µM total = µM a Ra
1. The atomic attenuation coefficient ( )+ µM b Rb + …
measures the probability of
absorption, per atom of absorbing The total mass attenuation coefficient
material, in barn (10–28 m2). for a compound, water, at 1 MeV, is:

2. The mass attenuation coefficient ( )µM water = 0.126  2 
measures the probability of absorption  18 
per gram of absorbing material in a
square centimeter of the beam + 0.0636  16 
(cm2·g–1).  18 

3. The linear attenuation coefficient = 0.0705 cm2 ⋅g–1
measures the probability of absorption
per centimeter of the absorbing where 0.126 and 0.0636 are the mass
material’s thickness (cm–1).
attenuation coefficients of hydrogen and
Linear Attenuation Coefficient
oxygen at 1 MeV. The relative abundance
The linear attenuation coefficient µL can
be expressed as: is figured using the relative atomic mass

(1) µL = µM × ρ Ar = 1 for hydrogen and Ar = 16 for
oxygen. Relative atomic mass (formerly

610 Radiographic Testing

called atomic weight) is the ratio of the sharp change occurs for K electrons is
average mass per atom of an element to called the K absorption edge and is used to
one twelfth of the mass of the atom of the identify the situation where kinetic
nuclide carbon 12. energy of the ejected K electron is zero.
Further increase of the photon energy
The same method can be used to causes the absorption to decrease almost
calculate the mass attenuation coefficient inversely with the cube of the energy.
at 0.02 MeV for air (a mixture), which
consists in percentages by weight
primarily of N2 (75.6 percent), O2
(23.1 percent) and Ar (1.3 percent). The
mass attenuation coefficients are as
follows: nitrogen, 0.598 cm2·g–1; oxygen,
0.840 cm2·g–1; and argon, 8.87 cm2·g–1.
Therefore the total mass attenuation
coefficient for air at 0.02 MeV is:

( )µM air = (0.598 × 0.756)
+ (0.840 × 0.231)
+ (8.87 × 0.013)

= 0.761 cm2 ⋅g–1

Linear Coefficient Tables

Tables 1 to 40 are based on a narrow beam
absorption. The calculated atomic, mass
and linear attenuation coefficients for
various elements are given in the energy
range of 0.01 to 30 MeV.

The tables were prepared for a previous
edition by the Radiation Physics
Committee of the American Society for
Nondestructive Testing, under the
direction of C. Robert Emigh of Los
Alamos National Laboratory, New Mexico.
The tabulations provide data for the
photoelectric component; data for the
pair production component, which
includes both nuclear and orbital electron
contributions; data for the scattering
component; and a correction for
electronic binding energies. Values were
obtained from G.R. White’s calculated
values in the Handbook of Radiology1 and
other sources.2-4 Corrections to these
values and values for other elements were
obtained by graphical interpolation. For
convenience, the values are presented to
no more than three significant figures,
although the estimated probable error is
no larger than one-half unit in the last
place, or three percent, whichever is
greater. The linear attenuation coefficients
are calculated with the density most
commonly used for the given element.

K Absorption Edge

Tables 21 to 40 include information on
the element’s K absorption edge. When
the transmitted photon energy reaches
the binding energy of a particular shell of
electrons, there is an abrupt increase in
the absorption. The energy at which this

Attenuation Coefficients 611

PART 2. Attenuation Coefficient Tables

TABLE 1. Attenuation coefficients for hydrogen (atomic number Z = 1).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 0.637 0.005 — 0.642 0.384 32.1 × 10–6
0.015 0.627 0.001 — 0.628 0.375 31.4 × 10–6
0.02 0.616 — 0.616 0.368 30.8 × 10–6
0.03 0.596 — — 0.596 0.356 29.8 × 10–6
0.04 0.578 — — 0.578 0.345 28.9 × 10–6
0.05 0.561 — — 0.561 0.335 28.1 × 10–6
0.06 0.546 — — 6.546 0.326 27.3 × 10–6
0.08 0.517 — — 0.517 0.309 25.9 × 10–6
0.10 0.493 — — 0.493 0.295 24.7 × 10–6
0.15 0.444 — — 0.444 0.265 22.2 × 10–6
0.20 0.407 — — 0.407 0.243 20.4 × 10–6
0.30 0.354 — — 0.354 0.212 17.8 × 10–6
0.40 0.317 — — 0.317 0.189 15.8 × 10–6
0.50 0.289 — — 0.289 0.173 14.5 × 10–6
0.60 0.268 — — 0.268 0.160 13.4 × 10–6
0.80 0.235 — — 0.235 0.140 11.7 × 10–6
1.0 0.211 — — 0.211 0.126 10.6 × 10–6
1.5 0.172 — — 0.172 0.103
2.0 0.146 — — 0.146 0.0873 8.63 × 10–6
3.0 0.115 — 0.001 0.116 0.0693 7.31 × 10–6
4.0 0.0960 — 0.0010 0.0970 0.0580 5.80 × 10–6
5.0 0.0828 — 0.0014 0.0842 0.0503 4.86 × 10–6
6.0 0.0732 — 0.0019 0.0751 0.0449 4.21 × 10–6
8.0 0.0599 — 0.0027 0.0626 0.0374 3.76 × 10–6
10.0 0.0510 — 0.0033 0.0543 0.0325 3.13 × 10–6
15.0 0.0377 — 0.0046 0.0423 0.0253 2.72 × 10–6
20.0 0.0302 — 0.0056 0.0358 0.0214 2.12 × 10–6
30.0 0.0220 — 0.0071 0.0291 0.0174 1.79 × 10–6
— 1.46 × 10–6

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 1.008.
b. Linear attenuation coefficient is calculated by using density ρ = 8.38 × 10–5 g·cm–3.

612 Radiographic Testing

TABLE 2. Attenuation coefficients for beryllium (atomic number Z = 4).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 3.54 5.42 — 8.96 0.599 1.09
0.015 3.01 1.39 — 4.40 0.294 0.535
0.02 2.77 0.52 — 3.29 0.220 0.400
0.03 2.53 0.13 — 2.66 0.178 0.324
0.04 2.38 0.05 — 2.43 0.162 0.295
0.05 2.28 0.02 — 2.30 0.154 0.280
0.06 2.21 0.01 — 2.22 0.148 0.269
0.08 2.09 — — 2.09 0.140 0.255
0.10 1.99 — — 1.99 0.133 0.242
0.15 1.78 — — 1.78 0.119 0.217
0.20 1.63 — — 1.63 0.109 0.198
0.30 1.41 — — 1.41 0.0943 0.172
0.40 1.27 — — 1.27 0.0849 0.155
0.50 1.16 — — 1.16 0.0775 0.141
0.60 1.07 — — 1.07 0.0715 0.130
0.80 0.940 — — 0.940 0.0628 0.114
1.0 0.845 — — 0.845 0.0565 0.103
1.5 0.686 — 0.001 0.687 0.459 0.0835
2.0 0.586 — 0.003 0.589 0.0394 0.0717
3.0 0.460 — 0.008 0.468 0.0313 0.0570
4.0 0.384 — 0.014 0.398 0.0266 0.0484
5.0 0.331 — 0.019 0.350 0.0234 0.0426
6.0 0.293 — 0.024 0.317 0.0212 0.0386
8.0 0.240 — 0.031 0.271 0.0181 0.0329
10 0.204 — 0.039 0.243 0.0162 0.0295
15 0.151 — 0.051 0.202 0.0135 0.0246
20 0.121 — 0.061 0.182 0.0122 0.0222
30 0.0880 — 0.075 0.163 0.0109 0.0198

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 9.013.
b. Linear attenuation coefficient is calculated by using density ρ = 1.82 g·cm–3.

Attenuation Coefficients 613

TABLE 3. Attenuation coefficients for carbon (atomic number Z = 6).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 6.90 38.6 — 45.5 2.28 5.06
0.015 5.30 10.2 — 15.5 0.778 1.73
0.02 4.64 — 0.429 0.952
0.03 4.04 3.91 — 8.55 0.252 0.559
0.04 3.71 0.99 — 5.03 0.205 0.455
0.05 3.53 0.38 — 4.09 0.186 0.413
0.06 3.38 0.18 — 3.71 0.175 0.389
0.08 3.18 0.10 — 3.48 0.162 0.360
0.10 3.02 0.04 — 3.22 0.153 0.340
0.15 2.69 0.02 — 3.04 0.135 0.300
0.20 2.46 — — 2.69 0.123 0.273
0.30 2.13 — — 2.46 0.107 0.238
0.40 1.90 — — 2.13 0.0953 0.212
0.50 1.74 — — 1.90 0.0873 0.194
0.60 1.61 — — 1.74 0.0808 0.179
0.80 1.41 — — 1.61 0.0707 0.157
1.0 1.27 — — 1.41 0.0637 0.141
1.5 1.03 — — 1.27 0.0517 0.115
2.0 0.878 — 0.006 1.03 0.0444 0.0986
3.0 0.691 — 0.018 0.884 0.0356 0.0790
4.0 0.576 — 0.031 0.709 0.0305 0.0677
5.0 0.497 — 0.042 0.607 0.0270 0.0599
6.0 0.439 — 0.052 0.539 0.0246 0.0546
8.0 0.359 — 0.068 0.491 0.0214 0.0475
10 0.306 — 0.083 0.427 0.0195 0.0433
15 0.226 — 0.110 0.389 0.0169 0.0375
20 0.181 — 0.130 0.336 0.0156 0.0346
30 0.132 — 0.160 0.311 0.0146 0.0324
— 0.292

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 12.010.
b. Linear attenuation coefficient for graphite form of carbon is calculated by using density ρ = 2.22 g·cm–3.

614 Radiographic Testing

TABLE 4. Attenuation coefficients for nitrogen (atomic number Z = 7).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 9.0 79.4 — 88.4 3.80 44.3 × 10–4
0.015 6.7 21.2 — 27.9 1.20 14.0 × 10–4
0.02 5.73 — 13.9 0.598
0.03 4.84 8.21 — 0.301 6.97 × 10–4
0.04 4.45 2.15 — 6.99 0.226 3.51 × 10–4
0.05 4.14 0.81 — 5.26 0.194 2.63 × 10–4
0.06 3.98 0.38 — 4.52 0.180 2.26 × 10–4
0.08 3.73 0.21 — 4.19 0.164 2.10 × 10–4
0.10 3.54 0.08 — 3.81 0.154 1.91 × 10–4
0.15 3.15 0.04 — 3.58 0.136 1.79 × 10–4
0.20 2.87 0.01 — 3.16 0.123 1.58 × 10–4
0.30 2.48 — — 2.87 0.107 1.43 × 10–4
0.40 2.22 — — 2.48 0.0955 1.25 × 10–4
0.50 2.02 — — 2.22 0.0869 1.11 × 10–4
0.60 1.87 — — 2.02 0.0804 1.01 × 10–4
0.80 1.65 — — 1.87 0.0710 0.937 × 10–4
1.0 1.48 — — 1.65 0.0637 0.827 × 10–4
1.5 1.20 — — 1.48 0.0516 0.742 × 10–4
2.0 1.03 — 0.01 1.20 0.0447 0.601 × 10–4
3.0 0.806 — 0.025 1.04 0.0357 0.521 × 10–4
4.0 0.672 — 0.042 0.831 0.0307 0.416 × 10–4
5.0 0.580 — 0.057 0.714 0.0274 0.358 × 10–4
6.0 0.512 — 0.071 0.637 0.0251 0.319 × 10–4
8.0 0.419 — 0.092 0.583 0.0220 0.292 × 10–4
10 0.357 — 0.111 0.511 0.0201 0.256 × 10–4
15 0.264 — 0.148 0.468 0.0177 0.234 × 10–4
20 0.212 — 0.174 0.412 0.0166 0.206 × 10–4
30 0.154 — 0.213 0.386 0.0158 0.193 × 10–4
— 0.367 0.184 × 10–4

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 14.088.
b. Linear attenuation coefficient is calculated by using density ρ = 1.165 × 10–3 g·cm–3.

Attenuation Coefficients 615

TABLE 5. Attenuation coefficients for oxygen (atomic number Z = 8).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 11.3 146 — 157 5.91 78.7 × 10–4
0.015 8.3 39.6 — 47.9 1.80 24.0 × 10–4
0.02 6.9 15.4 — 22.3 0.840 11.2 × 10–4
0.03 5.77 4.09 — 9.86 0.371
0.04 5.18 1.55 — 6.73 0.253 4.94 × 10–4
0.05 4.86 0.73 — 5.59 0.211 3.37 × 10–4
0.06 4.62 0.40 — 5.02 0.189 2.81 × 10–4
0.08 4.31 0.15 — 4.46 0.168 2.52 × 10–4
0.10 4.06 0.07 — 4.13 0.156 2.24 × 10–4
0.15 3.61 0.02 — 3.63 0.137 2.08 × 10–4
0.20 3.29 0.01 — 3.30 0.124 1.82 × 10–4
0.30 2.84 — — 2.84 0.107 1.65 × 10–4
0.40 2.54 — — 2.54 0.0957 1.43 × 10–4
0.50 2.31 — — 2.31 0.0870 1.27 ×10–4
0.60 2.14 — — 2.14 0.0806 1.16 × 10–4
0.80 1.88 — — 1.88 0.0708 1.07 × 10–4
1.0 1.69 — — 1.69 0.0636 0.943 × 10–4
1.5 1.37 — — 1.37 0.0516 0.847 × 10–4
2.0 1.17 — 0.01 1.18 0.0444 0.687 × 10–4
3.0 0.921 — 0.033 0.954 0.0359 0.591 × 10–4
4.0 0.768 — 0.054 0.822 0.0310 0.478 × 10–4
5.0 0.663 — 0.074 0.737 0.0278 0.413 × 10–4
6.0 0.586 — 0.091 0.677 0.0255 0.370 × 10–4
8.0 0.479 — 0.119 0.598 0.0225 0.340 × 10–4
10 0.408 — 0.143 0.551 0.0208 0.300 × 10–4
15 0.302 — 0.190 0.492 0.0185 0.277 × 10–4
20 0.242 — 0.224 0.466 0.0175 0.246 × 10–4
30 0.176 — 0.273 0.449 0.0169 0.233 × 10–4
0.225 × 10–4

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 16.000.
b. Linear attenuation coefficient is calculated by using density ρ = 1.332 × 10–3 g·cm–3.

616 Radiographic Testing

TABLE 6. Attenuation coefficients for sodium (atomic number Z = 11).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 20.6 588 — 609 16.0 15.5
0.015 14.0 169 — 183 4.79 4.65
0.02 11.3 — 2.06 2.00
0.03 67.5 — 78.8 0.707 0.686
0.04 8.91 18.1 — 27.0 0.385 0.374
0.05 7.71 — 14.7 0.272 0.264
0.06 7.07 7.0 — 10.4 0.225 0.218
0.08 6.67 3.3 — 0.179 0.174
0.10 6.08 1.90 — 8.57 0.157 0.152
0.15 5.66 0.74 — 6.82 0.134 0.130
0.20 5.01 0.32 — 5.98 0.120 0.117
0.30 4.54 0.09 — 5.10 0.103 0.100
0.40 3.92 0.04 — 4.58 0.0917 0.0890
0.50 3.50 0.01 — 3.93 0.0836 0.0812
0.60 3.19 — — 3.50 0.0770 0.0748
0.80 2.94 — — 3.19 0.0679 0.0659
1.0 2.59 — — 2.94 0.0608 0.0590
1.5 2.32 — — 2.59 0.0495 0.0481
2.0 1.89 — 0.02 2.32 0.0427 0.0415
3.0 1.61 — 0.06 1.89 0.0348 0.0338
4.0 1.27 — 0.10 1.63 0.0304 0.0295
5.0 1.06 — 0.139 1.33 0.0275 0.0267
6.0 0.911 — 0.170 1.16 0.0255 0.0248
8.0 0.805 — 0.221 1.05 0.0231 0.0224
10 0.659 — 0.266 0.975 0.0217 0.0211
15 0.561 — 0.351 0.880 0.0201 0.0195
20 0.415 — 0.413 0.827 0.0195 0.0189
30 0.333 — 0.500 0.766 0.0194 0.0188
0.242 — 0.746
— 0.742

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 22.997.
b. Linear attenuation coefficient is calculated by using density ρ = 0.971 g·cm–3.

Attenuation Coefficients 617

TABLE 7. Attenuation coefficients for magnesium (atomic number Z = 12).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 24.3 851 — 875 21.7 37.8
0.015 16.4 244 — 260 6.44 11.2
0.02 13.0 — 112 2.77
0.03 10.1 99.0 — 0.929 4.82
0.04 27.4 — 37.5 0.476 1.62
0.05 8.71 10.5 — 19.2 0.322 0.829
0.06 7.88 — 13.0 0.253 0.561
0.08 7.37 5.13 — 10.2 0.193 0.440
0.10 6.70 2.84 — 0.168 0.336
0.15 6.25 1.10 — 7.80 0.139 0.292
0.20 5.48 0.53 — 6.78 0.124 0.242
0.30 4.96 0.14 — 5.62 0.107 0.216
0.40 4.28 0.06 — 5.02 0.0949 0.186
0.50 3.82 0.02 — 4.30 0.0862 0.165
0.60 3.48 0.01 — 3.83 0.0798 0.150
0.80 3.22 — — 3.48 0.0699 0.139
1.0 2.82 — — 3.22 0.0627 0.122
1.5 2.53 — 0.01 2.82 0.0513 0.109
2.0 2.06 — 0.02 2.53 0.0441 0.0893
3.0 1.76 — 0.08 2.07 0.0362 0.0768
4.0 1.38 — 0.12 1.78 0.0315 0.0630
5.0 1.15 — 0.165 1.46 0.0287 0.0548
6.0 0.994 — 0.201 1.27 0.0268 0.0500
8.0 0.878 — 0.261 1.16 0.0243 0.0467
10 0.719 — 0.314 1.08 0.0229 0.0423
15 0.612 — 0.415 0.980 0.0215 0.0399
20 0.452 — 0.490 0.926 0.0211 0.0374
30 0.362 — 0.593 0.867 0.0212 0.0367
0.264 — 0.852 0.0369
— 0.857

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 24.32.
b. Linear attenuation coefficient is calculated by using density ρ = 1.741 g·cm–3.

618 Radiographic Testing

TABLE 8. Attenuation coefficients for aluminum (atomic number Z = 13).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 29 1170 — 1200 26.8 72.4
0.015 19 343 — 362 8.08 21.8
0.02 15 141 — 156 3.48
0.03 11.7 39.0 — 50.7 1.13 9.40
0.04 15.2 — 24.9 0.556 3.05
0.05 9.7 7.3 — 16.0 0.357 1.50
0.06 8.7 4.0 — 12.1 0.270 0.964
0.08 8.1 1.60 — 8.94 0.200 0.729
0.10 7.34 0.78 — 7.60 0.170 0.540
0.15 6.82 0.21 — 6.17 0.138 0.459
0.20 5.96 0.08 — 5.47 0.122 0.373
0.30 5.39 0.02 — 4.66 0.104 0.329
0.40 4.64 0.01 — 4.15 0.0927 0.281
0.50 4.14 — — 3.78 0.0844 0.250
0.60 3.78 — — 3.49 0.0779 0.228
0.80 3.49 — — 3.06 0.0683 0.210
1.0 3.06 — — 2.75 0.0614 0.184
1.5 2.75 — 0.01 2.24 0.0500 0.166
2.0 2.23 — 0.03 1.93 0.0431 0.135
3.0 1.90 — 0.09 1.59 0.0355 0.116
4.0 1.50 — 0.14 1.39 0.0310 0.0959
5.0 1.25 — 0.19 1.27 0.0284 0.0837
6.0 1.08 — 0.237 1.19 0.0266 0.0767
8.0 0.952 — 0.311 1.09 0.0243 0.0718
10 0.778 — 0.365 1.03 0.0230 0.0656
15 0.663 — 0.484 0.974 0.0217 0.0621
20 0.490 — 0.570 0.963 0.0215 0.0586
30 0.393 — 0.690 0.976 0.0218 0.0581
0.286 0.0589

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 26.98.
b. Linear attenuation coefficient is calculated by using density ρ = 2.70 g·cm–3.

Attenuation Coefficients 619

TABLE 9. Attenuation coefficients for silicon (atomic number Z = 14).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 33 1580 — 1610 34.5 81.1
0.015 22 470 — 492 10.6 24.9
0.02 17 194 — 211 10.6
0.03 12.8 54.4 — 67.2 4.53
0.04 10.8 21.4 — 32.2 1.44 3.38
0.05 10.3 — 19.9 0.691 1.62
0.06 9.6 5.8 — 14.7 0.427 1.00
0.08 8.9 2.3 — 10.3 0.315 0.740
0.10 8.0 1.10 — 8.48 0.221 0.519
0.15 7.38 0.29 — 6.73 0.182 0.428
0.20 6.44 0.12 — 5.94 0.144 0.338
0.30 5.82 0.04 — 5.05 0.127 0.298
0.40 5.01 0.02 — 4.48 0.108 0.254
0.50 4.46 — — 4.07 0.0961 0.226
0.60 4.07 — — 3.75 0.0873 0.205
0.80 3.75 — — 3.30 0.0804 0.189
1.0 3.30 — — 2.96 0.0708 0.166
1.5 2.96 — 0.01 2.41 0.0635 0.149
2.0 2.40 — 0.04 2.09 0.0517 0.121
3.0 2.05 — 0.10 1.71 0.0448 0.105
4.0 1.61 — 0.16 1.50 0.0367 0.0862
5.0 1.34 — 0.23 1.39 0.0322 0.0757
6.0 1.16 — 0.28 1.31 0.0298 0.0700
8.0 1.03 — 0.35 1.19 0.0281 0.0660
10 0.84 — 0.426 1.14 0.0255 0.0599
15 0.714 — 0.565 1.09 0.0245 0.0576
20 0.528 — 0.663 1.09 0.0234 0.0550
30 0.423 — 0.793 1.10 0.0234 0.0550
0.308 0.0236 0.0555

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 28.09.
b. Linear attenuation coefficient is calculated by using density ρ = 2.35 g·cm–3.

620 Radiographic Testing

TABLE 10. Attenuation coefficients for argon (atomic number Z = 18).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 56 4280 — 4340 65.4 10.9 × 10-2
0.015 36 1320 — 1360 20.5 3.41 × 10-2
0.02 27 — 1.48 × 10-2
0.03 19 561 — 588 8.87 0.459 × 10-2
0.04 15.6 164 — 183 2.76 0.201 × 10-2
0.05 13.6 — 1.21 0.113 × 10-2
0.06 12.4 64.5 — 80.1 0.682 0.0762 × 10-2
0.08 10.8 31.6 — 45.2 0.458 0.0451 × 10-2
0.10 18.0 — 30.4 0.271 0.0339 × 10-2
0.15 9.85 — 18.0 0.204 0.0236 × 10-2
0.20 8.43 7.2 — 13.5 0.142 0.0200 × 10-2
0.30 7.57 3.60 — 0.120 0.0165 × 10-2
0.40 6.48 0.98 — 9.41 0.0995 0.0146 × 10-2
0.50 5.76 0.41 — 7.98 0.0876 0.0132 × 10-2
0.60 5.24 0.12 — 6.60 0.0795 0.0122 × 10-2
0.80 4.84 0.05 — 5.81 0.0733 0.0106 × 10-2
1.0 4.24 0.03 — 5.27 0.0639 0.009 56 × 10-2
1.5 3.81 0.02 0.02 4.86 0.0575 0.007 80 × 10-2
2.0 3.09 — 0.06 4.24 0.0469 0.006 77 × 10-2
3.0 2.64 — 0.17 3.81 0.0407 0.005 62 × 10-2
4.0 2.07 — 0.27 3.11 0.0338 0.005 02 × 10-2
5.0 1.73 — 0.37 2.70 0.0302 0.004 66 × 10-2
6.0 1.49 — 0.45 2.24 0.0280 0.004 44 × 10-2
8.0 1.32 — 0.59 2.00 0.0267 0.004 19 × 10-2
10 1.08 — 0.691 1.86 0.0252 0.004 04 × 10-2
15 0.918 — 0.913 1.77 0.0243 0.003 99 × 10-2
20 0.679 — 1.06 1.67 0.0240 0.004 01 × 10-2
30 0.544 — 1.29 1.61 0.0241 0.004 24 × 10-2
0.396 — 1.59 0.0255
— 1.60
— 1.69

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 39.944.
b. Linear attenuation coefficient is calculated by using density ρ = 1.663 × 10–3 g·cm–3.

Attenuation Coefficients 621

TABLE 11. Attenuation coefficients for calcium (atomic number Z = 20).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 69 6380 — 6450 96.9 149
0.015 44 2010 — 2050 30.8 47.4
0.02 33 — 13.4 20.6
0.03 24 859 — 892 6.44
0.04 19 254 — 278 4.18 2.80
0.05 15.8 102 — 121 1.82 1.54
0.06 14.3 — 0.098 0.998
0.08 12.3 50.6 — 66.4 0.648 0.553
0.10 11.2 28.8 — 43.1 0.359 0.399
0.15 11.6 — 23.9 0.259 0.257
0.20 9.48 — 17.2 0.167 0.211
0.30 8.47 6.0 — 11.1 0.137 0.172
0.40 7.23 1.60 — 0.112 0.151
0.50 6.42 0.67 — 9.14 0.0978 0.136
0.60 5.84 0.20 — 7.43 0.0885 0.125
0.80 5.38 0.09 — 6.51 0.0813 0.109
1.0 4.72 0.05 — 5.89 0.0711 0.0981
1.5 4.24 0.03 0.02 5.41 0.0637 0.0798
2.0 3.43 0.01 0.07 4.73 0.0518 0.0695
3.0 2.93 — 0.21 4.24 0.0451 0.0581
4.0 2.30 — 0.33 3.45 0.0377 0.0521
5.0 1.92 — 0.45 3.00 0.0338 0.0488
6.0 1.66 — 0.55 2.51 0.0317 0.0465
8.0 1.46 — 0.72 2.25 0.0302 0.0445
10 1.20 — 0.84 2.11 0.0289 0.0431
15 1.02 — 1.12 2.01 0.0280 0.0436
20 0.755 — 1.31 1.92 0.0283 0.0445
30 0.605 — 1.57 1.86 0.0289 0.0465
0.440 — 1.88 0.0302
— 1.92
— 2.01

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 40.08.
b. Linear attenuation coefficient is calculated by using density ρ = 1.54 g·cm–3.

622 Radiographic Testing

TABLE 12. Attenuation coefficients for titanium (atomic number Z = 22).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 84 9150 — 9230 116 527
0.015 53 2900 — 2950 37.1 168
0.02 39 1250 — 1290 16.2
0.03 27 — 5.04 73.5
0.04 22 374 — 401 2.21 22.9
0.05 18.3 154 — 176 1.19 10.0
0.06 16.3 — 0.757
0.08 14.0 76.3 — 94.6 0.401 5.40
0.10 12.5 43.9 — 60.2 0.273 3.44
0.15 10.6 17.9 — 31.9 0.165 1.82
0.20 — 21.7 0.131 1.24
0.30 9.40 9.2 — 13.1 0.104 0.749
0.40 7.99 2.5 — 10.4 0.0908 0.595
0.50 7.09 1.04 — 0.0818 0.472
0.60 6.43 0.31 — 8.30 0.0754 0.412
0.80 5.94 0.13 — 7.22 0.0655 0.371
1.0 5.19 0.07 — 6.50 0.0587 0.342
1.5 4.66 0.05 0.02 5.99 0.0479 0.297
2.0 3.78 0.02 0.09 5.21 0.0416 0.266
3.0 3.22 0.01 0.25 4.67 0.0350 0.217
4.0 2.53 0.01 0.41 3.81 0.0317 0.189
5.0 2.11 — 0.54 3.31 0.0297 0.159
6.0 1.82 — 0.67 2.78 0.0287 0.144
8.0 1.61 — 0.86 2.52 0.0274 0.135
10 1.32 — 1.02 2.36 0.0269 0.130
15 1.12 — 1.34 2.28 0.0273 0.124
20 0.829 — 1.58 2.18 0.0282 0.122
30 0.664 — 1.90 2.14 0.0299 0.124
0.484 — 2.17 0.128
— 2.24 0.136
— 2.38

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 47.9.
b. Linear attenuation coefficient is calculated by using density ρ = 4.54 g·cm–3.

Attenuation Coefficients 623

TABLE 13. Attenuation coefficients for vanadium (atomic number Z = 23).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 92 10 700 — 10 800 128 763
0.015 58 3430 — 3490 41.3 246
0.02 43 1490 — 1530 18.1 108
0.03 29 449 — 478 5.65
0.04 23 185 — 208 2.46 33.7
0.05 19.6 92.7 — 112 1.32 14.7
0.06 17.4 53.3 — 70.7 0.836
0.08 14.8 21.8 — 36.6 0.443 7.87
0.10 13.3 11.1 — 24.4 0.289 4.98
0.15 11.1 3.1 — 14.2 0.168 2.58
0.20 1.27 — 11.1 0.131 1.72
0.30 9.85 0.38 — 8.74 0.103 1.00
0.40 8.36 0.16 — 7.57 0.0896 0.781
0.50 7.41 0.09 — 6.82 0.0807 0.614
0.60 6.73 0.06 — 6.26 0.0741 0.534
0.80 6.20 0.03 — 5.47 0.0647 0.481
1.0 5.44 0.02 — 4.90 0.0580 0.442
1.5 4.88 0.01 0.03 4.00 0.0473 0.386
2.0 3.96 — 0.09 3.46 0.0409 0.346
3.0 3.37 — 0.28 2.93 0.0347 0.282
4.0 2.65 — 0.44 2.65 0.0313 0.244
5.0 2.21 — 0.60 2.50 0.0296 0.207
6.0 1.90 — 0.73 2.41 0.0285 0.187
8.0 1.68 — 0.94 2.32 0.0274 0.176
10 1.38 — 1.12 2.29 0.0271 0.170
15 1.17 — 1.46 2.33 0.0276 0.163
20 0.867 — 1.74 2.44 0.0289 0.162
30 0.695 — 2.06 2.57 0.0304 0.164
0.506 0.172
0.181

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 50.95.
b. Linear attenuation coefficient is calculated by using density ρ = 5.96 g·cm–3.

624 Radiographic Testing

TABLE 14. Attenuation coefficients for chromium (atomic number Z = 24).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 101 12 500 — 12 600 146 1050
0.015 64 4040 — 4100 47.5 342
0.02 47 1760 — 1810 21.0 151
0.03 32 533 — 565 6.54 47.0
0.04 25 221 — 246 2.85 20.5
0.05 21 111 — 132 1.53 11.0
0.06 18.5 63.9 — 82.4 0.954 6.86
0.08 15.7 26.3 — 42.0 0.486 3.49
0.10 14.0 13.5 — 27.5 0.318 2.29
0.15 11.7 3.75 — 15.5 0.179 1.29
0.20 10.3 1.55 — 11.9 0.138 0.992
0.30 8.74 0.46 — 9.20 0.107 0.769
0.40 7.75 0.20 — 7.95 0.0921 0.662
0.50 7.03 0.11 — 7.14 0.0827 0.595
0.60 6.48 0.07 — 6.55 0.0758 0.545
0.80 5.67 0.03 — 5.70 0.0660 0.475
1.0 5.09 0.02 — 5.11 0.0592 0.426
1.5 4.13 0.01 0.03 4.17 0.0483 0.347
2.0 3.51 0.01 0.11 3.63 0.0420 0.302
3.0 2.76 — 0.30 3.06 0.0354 0.255
4.0 2.30 — 0.48 2.78 0.0322 0.232
5.0 1.99 — 0.65 2.64 0.0306 0.220
6.0 1.76 — 0.79 2.55 0.0295 0.212
8.0 1.44 — 1.02 2.46 0.0285 0.205
10 1.22 — 1.21 2.43 0.0281 0.202
15 0.905 — 1.59 2.50 0.0290 0.209
20 0.725 — 1.87 2.60 0.0301 0.216
30 0.528 — 2.24 2.77 0.0321 0.231

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 52.01.
b. Linear attenuation coefficient is calculated by using density ρ = 7.19 g·cm–3.

Attenuation Coefficients 625

TABLE 15. Attenuation coefficients for manganese (atomic number Z = 25).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 110 14 400 — 14 500 159 1180
0.015 70 4690 — 4760 52.2 388
0.02 51 2051 — 2100 23.0 171
0.03 34 626 — 660 7.24 53.8
0.04 27 263 — 290 3.18 23.6
0.05 22 132 — 154 1.69 12.6
0.06 19.7 76.2 — 95.9 1.05 7.80
0.08 16.6 31.4 — 48.0 0.527 3.92
0.10 14.7 16.2 — 30.9 0.339 2.52
0.15 12.2 4.51 — 16.7 0.183 1.36
0.20 10.8 1.88 — 12.7 0.139 1.03
0.30 9.13 0.56 — 9.69 0.106 0.788
0.40 8.09 0.24 — 8.33 0.0914 0.679
0.50 7.33 0.13 — 7.46 0.0818 0.608
0.60 6.76 0.08 — 6.84 0.0750 0.557’
0.80 5.91 0.04 — 5.95 0.0653 0.485
1.0 5.30 0.03 — 5.33 0.0585 0.435
1.5 4.30 0.01 0.03 4.34 0.0476 0.354
2.0 3.66 0.01 0.12 3.79 0.0416 0.309
3.0 2.88 — 0.33 3.21 0.0352 0.262
4.0 2.40 — 0.52 2.92 0.0320 0.238
5.0 2.07 — 0.70 2.77 0.0304 0.226
6.0 1.83 — 0.86 2.69 0.0295 0.219
8.0 1.50 — 1.11 2.61 0.0286 0.212
10 1.28 — 1.31 2.59 0.0284 0.211
15 0.943 — 1.72 2.66 0.0292 0.217
20 0.755 — 2.02 2.78 0.0305 0.227
30 0.55 — 2.43 2.98 0.0327 0.243

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 54.93.
b. Linear attenuation coefficient is calculated by using density ρ = 7.43 g·cm–3.

626 Radiographic Testing

TABLE 16. Attenuation coefficients for iron (atomic number Z = 26).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 120 16 500 — 16 600 179 1410
0.015 75 5380 — 5460 58.9 464
0.02 55 2380 — 2440 26.3 207
0.03 37 729 — 766 8.27 65.1
0.04 29 308 — 337 3.64 28.6
0.05 24 155 — 179 1.93 15.2
0.06 20.9 90.7 — 112 1.21 9.52
0.08 17.5 38.0 — 55.5 0.599 4.71
0.10 15.4 19.1 — 34.5 0.372 2.93
0.15 12.8 5.4 — 18.2 0.196 1.54
0.20 11.3 2.2 — 13.5 0.146 1.15
0.30 9.50 0.66 — 10.2 0.110 0.866
0.40 8.42 0.29 — 8.71 0.0940 0.740
0.50 7.63 0.16 — 7.79 0.0841 0.662
0.60 7.03 0.10 — 7.13 0.0769 0.605
0.80 6.15 0.05 — 6.20 0.0669 0.527
1.0 5.52 0.03 — 5.55 0.0599 0.471
1.5 4.46 0.02 0.03 4.51 0.0487 0.383
2.0 3.81 0.01 0.12 3.94 0.0425 0.334
3.0 2.99 — 0.35 3.34 0.0360 0.283
4.0 2.50 — 0.57 3.07 0.0331 0.260
5.0 2.15 — 0.76 2.91 0.0314 0.247
6.0 1.90 — 0.92 2.82 0.0304 0.239
8.0 1.56 — 1.20 2.76 0.0298 0.235
10 1.33 — 1.41 2.74 0.0296 0.233
15 0.981 — 1.86 2.84 0.0306 0.241
20 0.786 — 2.17 2.96 0.0319 0.251
30 0.572 — 2.61 3.18 0.0343 0.270

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 55.85.
b. Linear attenuation coefficient is calculated by using density ρ = 7.87 g·cm–3.

Attenuation Coefficients 627

TABLE 17. Attenuation coefficients for cobalt (atomic number Z = 27).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 130 18 800 — 18 900 193 1720
0.015 82 6170 — 6250 63.9 569
0.02 60 2760 — 2820 28.8 256
0.03 40 848 — 888 9.08 80.8
0.04 31 360 — 391 4.00 35.6
0.05 25 181 — 206 2.11 18.8
0.06 22 106 — 128 1.31 11.7
0.08 18.5 43.8 — 62.3 0.637 5.67
0.10 16.3 22.5 — 38.8 0.397 3.53
0.15 13.4 6.40 — 19.8 0.202 1.80
0.20 11.8 2.65 — 14.5 0.148 1.32
0.30 9.91 0.80 — 10.7 0.109 0.970
0.40 8.75 0.34 — 9.09 0.0929 0.827
0.50 7.94 0.19 — 8.13 0.0831 0.740
0.60 7.30 0.12 — 7.42 0.0758 0.675
0.80 6.39 0.06 — 6.45 0.0659 0.587
1.0 5.73 0.04 — 5.77 0.0590 0.525
1.5 4.64 0.02 0.03 4.69 0.0479 0.426
2.0 3.96 0.01 0.14 4.11 0.0420 0.374
3.0 3.11 0.01 0.38 3.50 0.0358 0.319
4.0 2.59 — 0.61 3.20 0.0327 0.291
5.0 2.24 — 0.82 3.06 0.0313 0.279
6.0 1.98 — 1.00 2.98 0.0305 0.271
8.0 1.62 — 1.29 2.91 0.0297 0.264
10 1.38 — 1.53 2.91 0.0297 0.264
15 1.02 — 2.00 3.02 0.0309 0.275
20 0.815 — 2.35 3.17 0.0324 0.288
30 0.594 — 2.82 3.41 0.0349 0.311

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 58.94.
b. Linear attenuation coefficient is calculated by using density ρ = 8.90 g·cm–3.

628 Radiographic Testing

TABLE 18. Attenuation coefficients for nickel (atomic number Z = 28).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 141 21 300 — 21 400 220 1950
0.015 89 7020 — 7110 73.0 646
0.02 65 3160 — 3230 33.2 294
0.03 43 984 — 1030 10.6 93.8
0.04 33 418 — 451 4.63 41.0
0.05 27 210 — 237 2.43 21.5
0.06 23 123 — 146 1.50 13.3
0.08 19.4 51.1 — 70.5 0.724 6.41
0.10 17.1 26.4 — 43.5 0.447 3.96
0.15 14.0 7.52 — 21.5 0.221 1.96
0.20 12.3 3.12 — 15.4 0.158 1.40
0.30 10.3 0.95 — 11.3 0.116 1.03
0.40 9.10 0.41 — 9.51 0.0977 0.865
0.50 8.24 0.22 — 8.46 0.0869 0.769
0.60 7.58 0.14 — 7.72 0.0793 0.702
0.80 6.63 0.07 — 6.70 0.0688 0.609
1.0 5.94 0.04 — 5.98 0.0614 0.543
1.5 4.81 0.02 0.04 4.87 0.0500 0.443
2.0 4.11 0.01 0.15 4.27 0.0439 0.389
3.0 3.22 0.01 0.41 3.64 0.0374 0.331
4.0 2.69 0.01 0.65 3.35 0.0344 0.304
5.0 2.32 — 0.88 3.20 0.0329 0.291
6.0 2.05 — 1.07 3.12 0.0320 0.283
8.0 1.68 — 1.39 3.07 0.0315 0.279
10 1.43 — 1.64 3.07 0.0315 0.279
15 1.06 — 2.14 3.20 0.0329 0.291
20 0.846 — 2.52 3.37 0.0346 0.306
30 0.616 — 3.02 3.64 0.0374 0.331

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 58.69.
b. Linear attenuation coefficient is calculated by using density ρ = 8.85 g·cm–3.

Attenuation Coefficients 629

TABLE 19. Attenuation coefficients for copper (atomic number Z = 29).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 150 23 600 — 23 800 226 2010
0.015 96 8000 — 8100 76.8 684
0.02 70 3580 — 3650 34.6 308
0.03 46 1120 — 1170 11.1 98.8
0.04 35 474 — 509 4.83 43.0
0.05 29 242 — 271 2.57 22.9
0.06 24 143 — 167 1.58 14.1
0.08 20.5 60.2 — 80.7 0.765 6.81
0.10 17.9 30.7 — 48.6 0.461 4.10
0.15 14.5 8.9 — 23.4 0.222 1.98
0.20 12.8 3.7 — 16.5 0.156 1.39
0.30 10.7 1.1 — 11.8 0.112 0.997
0.40 9.43 0.48 — 9.91 0.0940 0.837
0.50 8.54 0.26 — 8.80 0.0834 0.742
0.60 7.86 0.16 — 8.02 0.0760 0.676
0.80 6.87 0.08 — 6.95 0.0659 0.587
1.0 6.16 0.05 — 6.21 0.0589 0.524
1.5 4.98 0.02 0.04 5.04 0.0478 0.425
2.0 4.25 0.02 0.16 4.43 0.0420 0.374
3.0 3.34 0.01 0.44 3.79 0.0359 0.320
4.0 2.78 0.01 0.71 3.50 0.0332 0.295
5.0 2.40 0.01 0.95 3.36 0.0319 0.284
6.0 2.12 — 1.16 3.28 0.0311 0.277
8.0 1.74 — 1.48 3.22 0.0305 0.271
10 1.48 — 1.75 3.23 0.0306 0.272
15 1.09 — 2.29 3.38 0.0320 0.285
20 0.877 — 2.69 3.57 0.0339 0.302
30 0.638 — 3.23 3.87 0.0367 0.327

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 63.54.
b. Linear attenuation coefficient is calculated by using density ρ = 8.90 g·cm–3.

630 Radiographic Testing

TABLE 20. Attenuation coefficients for zinc (atomic number Z = 30).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 164 26 400 — 26 600 245 1750
0.015 103 8920 — 9020 83.1 593
0.02 4060 — 4140 38.2 272
0.03 75 1280 — 1330 12.3 87.7
0.04 49 549 — 586 5.40 38.5
0.05 37 276 — 305 2.81 20.0
0.06 29 163 — 189 1.74 12.4
0.08 26 68.5 — 90.0 0.829 5.91
0.10 21.5 35.5 — 54.2 0.499 3.56
0.15 18.7 10.2 — 25.4 0.234 1.67
0.20 15.2 4.28 — 17.5 0.161 1.15
0.30 13.2 1.29 — 12.4 0.114 0.83
0.40 11.1 0.56 — 10.3 0.0949 0.677
0.50 0.30 — 9.15 0.0843 0.601
0.60 9.77 0.19 — 8.33 0.0768 0.548
0.80 8.85 0.09 — 7.20 0.0663 0.473
1.0 8.14 0.06 — 6.44 0.0593 0.423
1.5 7.11 0.03 0.04 5.23 0.0482 0.344
2.0 6.38 0.02 0.17 4.59 0.0423 0.302
3.0 5.16 0.01 0.47 3.92 0.0361 0.258
4.0 4.40 0.01 0.74 3.63 0.0335 0.239
5.0 3.45 0.01 1.01 3.50 0.0323 0.230
6.0 2.88 0.01 1.22 3.43 0.0316 0.225
8.0 2.48 — 1.59 3.39 0.0312 0.223
10 2.20 — 1.87 3.40 0.0313 0.223
15 1.80 — 2.45 3.58 0.0330 0.235
20 1.53 — 2.87 3.78 0.0348 0.248
30 1.13 — 3.45 4.11 0.0379 0.270
0.906
0.660

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 65.38.
b. Linear attenuation coefficient is calculated by using density ρ = 7.133 g·cm–3.

Attenuation Coefficients 631

TABLE 21. Attenuation coefficients for germanium (atomic number Z = 32).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 189.0 3690 — 3880 32.2 173
3000 — 3170 26.3 141
0.011 12 170.0 27 500 — 27 700 230 1230
11 100 — 11 200 93.0 498
K 0.011 12 c 170.0 5130 — 5220 43.3 232
1640 — 1700 14.1
0.015 119.0 — 75.6
708 — 750 6.23 33.4
0.02 86.0 356 — 390 3.24 17.4
212 — 241 2.00 10.7
0.03 56.0 — 114 0.946
89.9 — 0.557 5.07
0.04 42.0 46.6 — 67.1 0.248 2.99
13.5 — 29.9 0.166 1.33
0.05 34.0 — 20.0 0.113 0.890
5.70 — 13.6 0.0938 0.606
0.06 29.0 1.74 — 11.3 0.0818 0.503
0.76 — 0.0744 0.438
0.08 23.7 0.41 — 9.86 0.0641 0.399
0.26 0.05 8.96 0.0571 0.344
0.10 20.5 0.13 0.19 7.72 0.0465 0.306
0.08 0.54 6.88 0.0408 0.249
0.15 16.4 0.04 0.86 5.60 0.0352 0.219
0.03 1.15 4.91 0.0327 0.189
0.20 14.3 0.01 1.39 4.24 0.0316 0.175
0.01 1.81 3.94 0.0310 0.169
0.30 11.9 0.01 2.13 3.81 0.0310 0.166
0.01 2.78 3.74 0.0312 0.166
0.40 10.5 0.01 3.25 3.74 0.0331 0.167
— 3.91 3.76 0.0350 0.177
0.50 9.45 — 3.99 0.0383 0.188
— 4.22 0.205
0.60 8.70 — 4.61

0.80 7.59

1.0 6.80

1.5 5.51

2.0 4.69

3.0 3.69

4.0 3.07

5.0 2.65

6.0 2.34

8.0 1.92

10 1.63

15 1.21

20 0.966

30 0.704

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 72.60.
b. Linear attenuation coefficient is calculated by using density ρ = 5.36 g·cm–3.

c. K = K absorption edge.

632 Radiographic Testing

TABLE 22. Attenuation coefficients for selenium (atomic number Z = 34).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 215 4410 — 4630 35.3 170.0
2530 — 2700 20.6 99.1
0.01268 172 22 300 — 22 500 172
13 600 — 13 700 105 827
K 0.012 68 c 172 6360 — 6460 49.3 505
2050 — 2110 16.1 237
0.015 137 —
895 — 942 7.19 77.4
0.02 98 454 — 492 3.75 34.6
270 — 302 2.30 18.0
0.03 63 116 — 142 1.08 11.1
— 0.629
0.04 47 60.2 — 82.5 0.270 5.19
17.7 — 35.4 0.172 3.03
0.05 38 — 22.6 0.114 1.30
7.45 — 15.0 0.0931 0.827
0.06 32 2.28 — 12.2 0.0809 0.548
1.00 — 10.6 0.0732 0.448
0.08 26 0.54 — 0.0629 0.389
0.34 0.06 9.60 0.0560 0.352
0.10 22.3 0.17 0.22 8.24 0.0455 0.303
0.11 0.61 7.34 0.0400 0.269
0.15 17.7 0.05 0.96 5.96 0.0347 0.219
0.03 1.30 5.24 0.0323 0.192
0.20 15.1 0.02 1.57 4.55 0.0315 0.167
0.01 2.04 4.23 0.0311 0.155
0.30 12.7 0.01 2.39 4.13 0.0312 0.152
0.01 3.12 4.07 0.0315 0.150
0.40 11.2 0.01 3.66 4.09 0.0336 0.150
0.01 4.39 4.13 0.0358 0.152
0.50 10.1 — 4.40 0.0392 0.162
— 4.69 0.172
0.60 9.26 — 5.14 0.189

0.80 8.07

1.0 7.23

1.5 5.85

2.0 4.99

3.0 3.92

4.0 3.26

5.0 2.82

6.0 2.49

8.0 2.04

10.0 1.73

15.0 1.28

20 1.03

30 0.748

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 78.96.
b. Linear attenuation coefficient is calculated by using density ρ = 4.81 g·cm–3.

c. K = K absorption edge.

Attenuation Coefficients 633

TABLE 23. Attenuation coefficients for zirconium (atomic number Z = 40).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 309 9220 — 9530 62.9 411
2820 — 3020 19.9 130
0.015 196 1790 — 1960 12.9
15 800 — 16 000 106 84.2
0.01760 171 11 000 — 11 100 73.3 692
3710 — 3800 25.1 479
K 0.017 60 c 171 1650 — 1720 11.4 164
—
0.02 140 850 — 901 5.95 74.4
512 — 555 3.67 38.9
0.03 88 226 — 259 1.71 24.0
117 — 145 0.958 11.2
0.04 65 — 0.377
35.3 — 57.1 0.223 6.26
0.05 51 15.2 — 33.7 0.131 2.46
— 19.9 0.102 1.46
0.06 43 4.68 — 15.4 0.0859 0.855
2.08 — 13.0 0.0773 0.666
0.08 33 1.13 — 11.7 0.0653 0.561
0.71 0.08 0.0579 0.505
0.10 28 0.36 0.32 9.89 0.0468 0.426
0.23 0.85 8.76 0.0414 0.378
0.15 21.8 0.11 1.35 7.08 0.0363 0.306
0.07 1.80 6.27 0.0345 0.270
0.20 18.5 0.04 2.17 5.50 0.0339 0.237
0.03 2.79 5.22 0.0338 0.225
0.30 15.2 0.02 3.28 5.13 0.0343 0.221
0.02 4.26 5.12 0.0352 0.221
0.40 13.3 0.01 5.00 5.20 0.0382 0.224
0.01 6.00 5.33 0.0410 0.230
0.50 11.9 0.01 5.78 0.0454 0.249
— 6.21 0.268
0.60 11.0 — 6.88 0.296

0.80 9.53

1.0 8.53

1.5 6.89

2.0 5.88

3.0 4.61

4.0 3.84

5.0 3.31

6.0 2.93

8.0 2.40

10 2.04

15 1.51

20 1.21

30 0.88

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 91.22.
b. Linear attenuation coefficient is calculated by using density ρ = 6.53 g·cm–3.

c. K = K absorption edge.

634 Radiographic Testing

TABLE 24. Attenuation coefficients for niobium (atomic number Z = 41).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 326 10 300 — 10 600 68.7 589
3140 — 3350 21.7 186
0.015 208 1490 — 1640 10.6
— 85.6 90.8
0.01902 152 13 000 — 13 200 77.8 734
11 900 — 12 000 27.0 667
K 0.019 02 c 152 — 12.2 231
4070 — 4160 105
0.02 148 1810 — 1880 6.42
— 3.94 55.0
0.03 93 936 — 990 1.85 33.8
563 — 608 1.03 15.9
0.04 69 251 — 286 0.401
130 — 159 0.233 8.83
0.05 54 — 0.135 3.44
39.3 — 61.8 0.103 2.00
0.06 45 16.9 — 36.0 0.0882 1.16
— 20.8 0.0778 0.883
0.08 35 5.23 — 15.9 0.0661 0.756
2.32 0.09 13.6 0.0584 0.667
0.10 29 1.25 0.33 12.0 0.0473 0.566
0.79 0.90 10.2 0.0417 0.500
0.15 22.5 0.40 1.41 0.0368 0.405
0.26 1.89 9.01 0.0350 0.357
0.20 19.1 0.13 2.27 7.30 0.0345 0.315
0.08 2.93 6.43 0.0343 0.300
0.30 15.6 0.05 3.43 5.68 0.0351 0.296
0.03 4.48 5.39 0.0359 0.294
0.40 13.6 0.03 5.24 5.32 0.0392 0.301
0.02 6.27 5.29 0.0421 0.308
0.50 12.3 0.02 5.41 0.0465 0.336
0.01 5.53 0.361
0.60 11.2 0.01 6.04 0.398
0.01 6.49
0.80 9.78 — 7.17

1.0 8.75

1.5 7.08

2.0 6.02

3.0 4.73

4.0 3.95

5.0 3.40

6.0 3.00

8.0 2.46

10 2.09

15 1.55

20 1.24

30 0.90

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 92.91.
b. Linear attenuation coefficient is calculated by using density ρ = 8.57 g·cm–3.

c. K = K absorption edge.

Attenuation Coefficients 635

TABLE 25. Attenuation coefficients for molybdenum (atomic number Z = 42).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 340 11 400 — 11 700 73.5 750
3480 — 3700 23.2 240
0.015 220 1510 — 1670 10.5 107
— 82.9 846
0.02004 160 13 000 — 13 200 28.2 288
4390 — 4490 12.7 130
K 0.020 04 c 160 1960 — 2030
1030 — 1090 6.85 69.9
0.03 98 620 — 667 4.19 42.7
274 — 310 1.95 19.9
0.04 71 144 — 174 1.09 11.1
43.4 — 66.6 0.418
0.05 56 18.7 — 38.5 0.242 4.26
5.8 — 21.9 0.138 2.47
0.06 47 2.6 — 16.6 0.104 1.41
1.4 — 14.0 0.0879 1.06
0.08 36 0.88 — 12.4 0.0779 0.897
0.45 — 10.5 0.0659 0.795
0.10 30 0.29 0.09 9.25 0.0581 0.672
0.14 0.35 7.48 0.0470 0.593
0.15 23.2 0.09 0.94 6.59 0.0414 0.479
0.05 1.50 5.82 0.0365 0.422
0.20 19.8 0.04 1.98 5.57 0.0350 0.372
0.03 2.38 5.49 0.0345 0.357
0.30 16.1 0.01 3.06 5.47 0.0344 0.352
0.01 3.59 5.59 0.0351 0.351
0.40 14.0 0.01 4.68 5.74 0.0360 0.358
0.01 5.47 6.28 0.0394 0.367
0.50 12.6 0.01 6.57 6.75 0.0424 0.402
— 7.49 0.0470 0.432
0.60 11.5 0.479

0.80 10.0

1.0 8.96

1.5 7.25

2.0 6.15

3.0 4.83

4.0 4.03

5.0 3.48

6.0 3.08

8.0 2.52

10 2.14

15 1.59

20 1.27

30 0.92

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 95.95.
b. Linear attenuation coefficient is calculated by using density ρ = 10.2 g·cm–3.

c. K = K absorption edge.

636 Radiographic Testing

TABLE 26. Attenuation coefficients for silver (atomic number Z = 47).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 443 18 500 — 18 900 106 1110
5670 — 5960 33.3 349
0.015 285 2460 — 2660 14.9 156
1180 — 1340 7.48 78.5
0.02 202 — 57.0 598
10 000 — 10 200 37.5 393
0.02559 156 6590 — 6720 17.0 178
2960 — 3050 9.22 96.7
K 0.025 59 c 156 1580 — 1650 5.64 59.2
952 — 1010 2.63 27.6
0.03 125 427 — 471 1.46 15.3
225 — 261 0.534 5.60
0.04 91 68.6 — 95.7 0.296 3.11
30.4 — 53.0 0.155 1.63
0.05 70 9.49 — 27.8 0.112 1.17
4.27 — 20.1 0.0922 0.967
0.06 57 2.32 — 16.5 0.0810 0.850
1.46 — 14.5 0.0676 0.709
0.08 44 0.75 — 12.1 0.0592 0.621
0.48 0.12 10.6 0.0474 0.497
0.10 36 0.24 0.45 8.49 0.0419 0.440
0.15 1.20 7.51 0.0375 0.393
0.15 27.1 0.09 1.87 6.72 0.0360 0.378
0.06 2.50 6.45 0.0360 0.378
0.20 22.6 0.05 2.99 6.45 0.0361 0.379
0.04 3.81 6.47 0.0372 0.390
0.30 18.3 0.03 4.47 6.66 0.0385 0.404
0.02 5.81 6.89 0.0424 0.445
0.40 15.8 0.01 6.79 7.59 0.0459 0.481
0.01 8.14 8.22 0.0513 0.538
0.50 14.2 0.01 9.18

0.60 13.0

0.80 11.3

1.0 10.1

1.5 8.13

2.0 6.91

3.0 5.43

4.0 4.52

5.0 3.90

6.0 3.44

8.0 2.82

10.0 2.40

15.0 1.77

20.0 1.42

30.0 1.03

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 107.88.
b. Linear attenuation coefficient is calculated by using density ρ = 10.49 g·cm–3.

c. K = K absorption edge.

Attenuation Coefficients 637

TABLE 27. Attenuation coefficients for cadmium (atomic number Z = 48).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 466 20 200 — 20 700 111 960
6220 — 6540 35.1 304
0.015 322 2700 — 2910 15.6 135
1170 — 1330 7.13
0.02 212 9700 — 9860 52.8 61.7
7080 — 7210 38.6 457
0.02676 159 3210 — 3310 17.7 334
1710 — 1780 9.54 153
K 0.026 76 c 159 1030 — 1090 5.84
461 — 507 2.72 82.5
0.03 131 245 — 283 1.52 50.5
74.9 — 103 0.552 23.5
0.04 95 33.4 — 56.7 0.304 13.1
10.4 — 29.1 0.156
0.05 73 4.66 — 20.9 0.112 4.77
2.55 — 17.1 0.0917 2.63
0.06 60 1.60 — 14.9 0.0799 1.35
0.83 — 12.3 0.0659 0.969
0.08 46 0.53 — 10.8 0.0579 0.793
0.26 0.13 8.69 0.0466 0.691
0.10 38 0.17 0.47 7.70 0.0413 0.570
0.10 1.25 6.89 0.0369 0.501
0.15 27.9 0.07 1.95 6.64 0.0356 0.403
0.05 2.61 6.64 0.0356 0.357
0.20 23.3 0.05 3.12 6.68 0.0358 0.319
0.03 3.98 6.89 0.0369 0.308
0.30 18.7 0.03 4.66 7.14 0.0383 0.308
0.02 6.05 7.88 0.0422 0.310
0.40 16.2 0.01 7.08 8.54 0.0458 0.319
0.01 8.47 9.54 0.0511 0.331
0.50 14.5 0.365
0.396
0.60 13.3 0.442

0.80 11.5

1.0 10.3

1.5 8.30

2.0 7.06

3.0 5.54

4.0 4.62

5.0 3.98

6.0 3.51

8.0 2.88

10 2.45

15 1.81

20 1.45

30 1.06

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 112.41.
b. Linear attenuation coefficient is calculated by using density ρ = 8.65 g·cm–3.

c. K = K absorption edge.

638 Radiographic Testing

TABLE 28. Attenuation coefficients for tin (atomic number Z = 50).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 510 24 000 — 24 500 124 905
7410 — 7740 39.3 287
0.015 330 3220 — 3460 17.6 128
1050 — 1200 6.09
0.02 240 8580 — 8730 44.3 44.5
8150 — 8290 42.1 323
0.02925 150 3700 — 3800 19.3 307
1990 — 2070 10.5 141
K 0.029 25 c 150 1210 — 1280 6.50
539 — 588 2.98 76.7
0.03 143 286 — 326 1.65 47.5
88.8 — 118 0.599 21.8
0.04 103 39.3 — 63.9 0.324 12.0
12.4 — 32.1 0.163
0.05 79 5.6 — 22.6 0.115 4.37
3.0 — 18.2 0.0924 2.37
0.06 65 1.9 — 15.7 0.0797 1.19
1.0 — 13.0 0.0660 0.840
0.08 49 0.64 — 11.3 0.0574 0.675
0.32 0.14 9.11 0.0462 0.582
0.10 40 0.20 0.51 8.07 0.0410 0.482
0.12 1.35 7.23 0.0367 0.419
0.15 29.6 0.08 2.14 7.02 0.0356 0.337
0.06 2.82 7.02 0.0356 0.299
0.20 24.6 0.05 3.37 7.08 0.0359 0.268
0.04 4.29 7.32 0.0372 0.260
0.30 19.7 0.03 5.04 7.62 0.0387 0.260
0.02 6.54 8.45 0.0429 0.262
0.40 17.0 0.01 7.63 9.15 0.0464 0.272
0.01 9.15 10.3 0.0523 0.283
0.50 15.2 0.313
0.339
0.60 13.8 0.382

0.80 12.0

1.0 10.7

1.5 8.65

2.0 7.36

3.0 5.76

4.0 4.80

5.0 4.14

6.0 3.66

8.0 2.99

10 2.55

15 1.89

20 1.51

30 1.10

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 118.70.
b. Linear attenuation coefficient is calculated by using density ρ = 7.30 g·cm–3.

c. K = K absorption edge.

Attenuation Coefficients 639

TABLE 29. Attenuation coefficients for antimony (atomic number Z = 51).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 535 25 900 — 26 400 131 867
8010 — 8350 41.3 273
0.015 344 3490 — 3730 18.5 122
1000 — 1150 5.69
0.02 244 8140 — 8290 41.0 37.7
3970 — 4080 20.2 271
0.03050 148 2140 — 2220 11.0 134
1300 — 1370 6.78
K 0.030 50c 148 580 — 631 3.12 72.8
311 — 353 1.75 44.9
0.04 108 93.5 — 124 0.614 20.7
42.8 — 67.9 0.336 11.6
0.05 82 13.5 — 33.6 0.166
6.11 — 23.4 0.116 4.06
0.06 67 3.34 — 18.8 0.0930 2.22
2.09 — 16.2 0.0802 1.10
0.08 51 1.09 — 13.4 0.0663 0.768
0.71 — 11.6 0.0574 0.616
0.10 42 0.34 0.15 9.31 0.0461 0.531
0.22 0.54 8.27 0.0409 0.439
0.15 30.4 0.13 1.42 7.44 0.0368 0.380
0.09 2.21 7.21 0.0357 0.305
0.20 25.1 0.07 2.95 7.25 0.0359 0.271
0.06 3.51 7.30 0.0361 0.244
0.30 20.1 0.04 4.47 7.57 0.0375 0.236
0.03 5.22 7.85 0.0388 0.238
0.40 17.3 0.02 6.79 8.73 0.0432 0.239
0.01 7.90 9.45 0.0468 0.248
0.50 15.5 0.01 9.49 10.6 0.0524 0.257
0.286
0.60 14.1 0.310
0.347
0.80 12.3

1.0 10.9

1.5 8.82

2.0 7.51

3.0 5.89

4.0 4.91

5.0 4.23

6.0 3.73

8.0 3.06

10 2.60

15 1.92

20 1.54

30 1.12

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 121.76.
b. Linear attenuation coefficient is calculated by using density ρ = 6.62 g·cm–3.

c. K = K absorption edge.

640 Radiographic Testing

TABLE 30. Attenuation coefficients for iodine (atomic number Z = 53).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 590 29 800 — 30 400 144 710
9360 — 9740 46.2 228
0.015 380 4130 — 4400 20.9 103
1260 — 1420 6.74
0.02 270 933 — 1080 5.13 33.2
7510 — 7660 36.4 2S.3
0.03 164 4490 — 4610 21.9
2470 — 2560 12.2 179
0.03323 150 1500 — 1570 7.45 108
677 — 731 3.47
K 0.033 23 c 150 360 — 404 1.92 60.1
113 — 145 0.688 36.7
0.04 117 50.0 — 76.5 0.363 17.1
16.0 — 37.0 0.176
0.05 89 7.2 — 25.3 0.120 9.47
3.9 — 20.1 0.0954 3.39
0.06 72 2.5 — 17.3 0.0821 1.79
1.3 — 14.1 0.0669 0.868
0.08 54 0.84 — 12.2 0.0579 0.592
0.41 0.17 9.76 0.0463 0.470
0.10 44 0.26 0.59 8.66 0.0411 0.405
0.16 1.53 7.79 0.0370 0.330
0.15 32 0.11 2.41 7.61 0.0361 0.285
0.08 3.17 7.64 0.0363 0.228
0.20 26.5 0.07 3.78 7.73 0.0367 0.203
0.05 4.81 8.03 0.0381 0.182
0.30 21.0 0.04 5.63 8.37 0.0397 0.178
0.02 7.30 9.32 0.0442 0.179
0.40 18.1 0.01 8.51 10.1 0.0479 0.181
0.01 10.2 11.4 0.0541 0.188
0.50 16.2 0.196
0.218
0.60 14.8 0.236
0.267
0.80 12.8

1.0 11.4

1.5 9.18

2.0 7.81

3.0 6.10

4.0 5.09

5.0 4.39

6.0 3.88

8.0 3.17

10 2.70

15 2.00

20 1.60

30 1.17

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 126.92.
b. Linear attenuation coefficient is calculated by using density ρ = 4.93 g·cm–3.

c. K = K absorption edge.

Attenuation Coefficients 641

TABLE 31. Attenuation coefficients for cesium (atomic number Z = 55).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 633 34 700 — 35 300 160 299
11 000 — 11 400 51.7 96.7
0.015 411 — 23.2 43.4
4830 — 5120 7.52 14.1
0.02 290 1480 — 1660 4.67 8.73
— 1030 32.9 61.5
0.03 177 881 — 7250 24.0 44.9
7100 — 5290 13.3 24.9
0.036 03 146 5160 — 2940 8.16 15.3
2840 — 1800 3.73 6.98
K 0.036 03 c 146 1720 — 2.09 3.91
— 823 0.739 1.38
0.04 127 765 — 461 0.391 0.731
414 — 163 0.184 0.344
0.05 96 129 — 0.124 0.232
— 86.2 0.0970 0.181
0.06 78 58.4 — 40.5 0.0825 0.154
18.6 — 27.3 0.0671 0.125
0.08 58 — 21.4 0.0580 0.108
8.46 0.18 18.2 0.0462 0.0864
0.10 47 4.64 0.64 14.8 0.0410 0.0767
2.93 1.66 12.8 0.0372 0.0696
0.15 34 1.54 2.59 10.2 0.0363 0.0679
1.00 3.42 0.0366 0.0684
0.20 27.8 0.49 4.07 9.05 0.0371 0.0694
0.31 5.17 8.20 0.0387 0.0724
0.30 21.9 0.18 6.04 8.01 0.0403 0.0754
0.13 7.82 8.08 0.0450 0.0842
0.40 18.8 0.10 9.12 8.19 0.0490 0.0916
0.08 10.9 8.53 0.0548 0.102
0.50 16.8 0.06 8.90
0.05 9.92
0.60 15.3 0.03 10.8
0.02 12.1
0.80 13.3 0.01

1.0 11.8

1.5 9.53

2.0 8.10

3.0 6.36

4.0 5.29

5.0 4.56

6.0 4.04

8.0 3.30

10 2.81

15 2.07

20 1.66

30 1.21

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 132.91.
b. Linear attenuation coefficient is calculated by using density ρ = 1.87 g·cm–3.

c. K = K absorption edge.

642 Radiographic Testing

TABLE 32. Attenuation coefficients for barium (atomic number Z = 56).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.01 662 37 000 — 37 700 165 624
11 900 — 12 300 53.9 204
0.015 371 — 24.1
5190 — 5490 7.81 91.1
0.02 303 1590 — 1780 4.31 29.5
— 30.1 16.3
0.03 185 837 — 982 24.7 114
6720 — 6870 13.7 93.4
0.03748 145 5510 — 5640 8.42 51.8
3030 — 3130 3.84 31.8
K 0.037 48 c 145 1834 — 1920 2.16 14.5
— 0.759
0.04 132 815 — 875 0.400 8.16
444 — 493 0.186 2.87
0.05 100 138 — 173 0.124 1.51
— 0.0969 0.703
0.06 81 62.8 — 91.2 0.0825 0.469
20.0 — 42.4 0.0667 0.366
0.08 60 — 28.3 0.0579 0.312
9.14 0.19 22.1 0.0456 0.252
0.10 49 5.02 0.67 18.8 0.0406 0.219
3.18 1.73 15.2 0.0368 0.172
0.15 35 1.67 2.68 13.2 0.0360 0.153
1.09 3.59 10.4 0.0366 0.139
0.20 28.4 0.53 4.21 0.0369 0.136
0.34 5.35 9.26 0.0385 0.138
0.30 22.4 0.20 6.26 8.40 0.0402 0.139
0.14 8.09 8.21 0.0447 0.146
0.40 19.2 0.11 9.45 8.35 0.0491 0.152
0.09 11.3 8.41 0.0553 0.169
0.50 17.1 0.07 8.77 0.186
0.05 9.17 0.209
0.60 15.6 0.03 10.2
0.02 11.2
0.80 13.5 0.02 12.6

1.0 12.1

1.5 9.70

2.0 8.25

3.0 6.47

4.0 5.39

5.0 4.65

6.0 4.11

8.0 3.35

10 2.86

15 2.11

20 1.69

30 1.23

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 137.36.
b. Linear attenuation coefficient is calculated by using density ρ = 3.78 g·cm–3.

c. K = K absorption edge.

Attenuation Coefficients 643

TABLE 33. Attenuation coefficients for thulium (atomic number Z = 69).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.015 705 27 400 — 28 100 100 935
12 200 — 12 700 45.2 423
0.02 496 — 14.5 136
3790 — 4090 6.76
0.03 300 1690 — 1900 3.70 63.2
— 1040 2.22 34.6
0.04 210 884 — 14.3 20.8
497 — 623 14.2 134
0.05 156 3880 — 4010 6.54 133
3860 — 3980 3.70 61.1
0.059 45 126 1750 — 1840 1.28 34.6
970 — 1040 0.647 12.0
K 0.059 45 c 126 313 — 0.271
144 — 361 0.166 6.05
0.06 124 — 182 0.121 2.53
47.2 — 0.0985 1.55
0.08 89 22.4 — 76.2 0.0758 1.13
12.5 — 46.8 0.0637 0.921
0.10 74 0.33 34.1 0.0487 0.709
8.05 1.11 27.7 0.0434 0.596
0.15 48 4.35 2.73 21.3 0.0398 0.455
2.85 4.15 17.9 0.0398 0.406
0.20 38 1.38 5.41 13.7 0.0405 0.372
0.89 6.36 12.2 0.0413 0.372
0.30 29.0 0.51 7.97 11.2 0.0438 0.379
0.36 9.27 11.2 0.0459 0.386
0.40 24.4 0.28 11.9 11.4 0.0519 0.410
0.23 13.9 11.6 0.0569 0.429
0.50 21.6 0.17 16.5 12.3 0.0644 0.485
0.13 12.9 0.532
0.60 19.6 0.08 14.6 0.602
0.06 16.0
0.80 16.9 0.04 18.1

1.0 15.0

1.5 12.0

2.0 10.2

3.0 7.99

4.0 6.65

5.0 5.73

6.0 5.05

8.0 4.14

10 3.52

15 2.60

20 2.08

30 1.52

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 169.4.
b. Linear attenuation coefficient is calculated by using density ρ = 9.35 g·cm–3.

c. K = K absorption edge.

644 Radiographic Testing

TABLE 34. Attenuation coefficients for tantalum (atomic number Z = 73).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.015 808 34 000 — 34 800 116 1930
15 200 — 15 800 52.6 873
0.02 569 — 17.0 282
4750 — 5090 7.86 130
0.03 342 2120 — 2360 4.30 71.4
1110 — 1290 2.59 43.0
0.04 238 — 1.88 31.2
638 — 778 11.6 193
0.05 176 440 — 564 7.46 124
3360 — 3480 4.20 69.7
0.06 140 2140 — 2240 1.47 24.4
1180 — 1260 0.733 12.2
0.067 51 124 387 — 440 0.302 5.01
179 — 220 0.182 3.02
K 0.067 51 c 124 — 0.130 2.16
59.3 — 90.6 0.104 1.73
0.08 101 28.4 — 54.5 0.0783 1.30
15.9 — 38.9 0.0653 1.08
0.10 79 10.3 0.39 31.2 0.0496 0.823
1.28 23.5 0.0440 0.730
0.15 53 5.60 3.08 19.6 0.0406 0.674
3.69 4.67 14.9 0.0406 0.674
0.20 41 1.78 6.06 13.2 0.0416 0.691
1.15 7.08 12.2 0.0423 0.702
0.30 31.1 0.66 8.86 12.2 0.0446 0.740
0.47 10.3 12.5 0.0473 0.785
0.40 26.1 0.36 13.2 12.7 0.0536 0.890
0.29 15.4 13.4 0.0590 0.979
0.50 23.0 0.21 18.4 14.2 0.0670 1.11
0.17 16.1
0.60 20.9 0.11 17.7
0.08 20.1
0.80 17.9 0.05

1.0 15.9

1.5 12.7

2.0 10.8

3.0 8.45

4.0 7.04

5.0 6.06

6.0 5.35

8.0 4.37

10 3.72

15 2.75

20 2.20

30 1.61

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 180.88.
b. Linear attenuation coefficient is calculated by using density ρ = 16.6 g·cm–3.

c. K = K absorption edge.

Attenuation Coefficients 645

TABLE 35. Attenuation coefficients for tungsten (atomic number Z = 74).

______A_t_te__n_u_a_t_io__n_C__o_e_f_fi_c_i_e_n_t_µ_________

Energy _______C__r_o_s_s_S_e_c_t_i_o_n__(1__0_–2_8__m__2)____ Atomic Mass a Linear b
(MeV) Scattering Photoelectric Pair
(10–28 m2) (cm2·g–1) (cm–1)

0.015 840 36 000 — 36 800 121 2260
16 000 — 16 600 54.4 1020
0.02 590 — 17.7
5040 — 5390 8.09 331
0.03 350 2220 — 2470 4.39 151
1160 — 1340 2.68
0.04 245 — 1.83 82.1
674 — 819 11.0 50.1
0.05 180 437 — 559 7.70 34.2
3230 — 3350 4.36 206
0.06 145 2250 — 2350 1.51 144
1250 — 1330 0.747 81.5
0.069 64 122 408 — 462 0.310 28.2
186 — 228 0.184 14.0
K 0.069 64 c 122 — 0.131
63.1 — 94.6 0.105 5.80
0.08 104 29.8 — 56.3 0.0790 3.44
16.7 — 40.1 0.0655 2.45
0.10 80 11.0 0.40 32.2 0.0498 1.96
1.32 24.1 0.0439 1.48
0.15 54 5.9 3.20 20.0 0.0410 1.22
3.9 4.81 15.2 0.0406 0.931
0.20 42 1.9 6.23 13.4 0.0416 0.821
1.2 7.34 12.5 0.0426 0.767
0.30 31.5 0.71 9.06 12.4 0.0449 0.759
0.50 10.6 12.7 0.0478 0.778
0.40 26.5 0.38 13.5 13.0 0.0537 0.797
0.31 15.7 13.7 0.0590 0.840
0.50 23.4 0.23 18.8 14.6 0.0672 0.894
0.18 16.4 1.00
0.60 21.2 0.11 18.0 1.10
0.08 20.5 1.26
0.80 18.2 0.06

1.0 16.1

1.5 12.9

2.0 10.9

3.0 8.57

4.0 7.10

5.0 6.13

6.0 5.42

8.0 4.43

10 3.77

15 2.79

20 2.24

30 1.63

a. Mass attenuation coefficient is calculated by using relative atomic mass Ar = 183.92.
b. Linear attenuation coefficient is calculated by using density ρ = 18.7 g·cm–3.

c. K = K absorption edge.

646 Radiographic Testing