NBSIR 83-2646

Characterization of

Window Materials

j AlllDb EblSS?

Microwave

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Measurement Laboratory

Center for Materials Science

Inorganic Materials Division

Washington, DC 20234

May-October S 982

Interim Report

Issued January 1 983

Task Cede: NggGAXAH/ Missile Systems/ X-Ray Ha r dness

Work Unit: 00043/ Materials Characterization

Dr eparea for " UC ' :fense Nuclear Agency

ll)j ashington, DC 20300

. U56

83-2646

1463

NATIONAL BV:u.AU, OF STANDARD^

FEB 7 1333

f\oV CvCC

NBSIR 83-2646

CHARACTERIZATION OF MICROWAVE

WINDOW MATERIALS

H.P.R. Frederikse, A.L. Dragoo, and A.H. Kahn

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Measurement Laboratory

Center for Materials Science

Inorganic Materials Division

Washington, DC 20234

W.R. Hosier

WRH Co.

Poolesville, MD

May-October 1 982

Interim Report

Task Code: NggQAXAH/ Missile Systems/X-Ray Hardness

Work Unit: 00043/ Materials Characterization

Prepared for Defense Nuclear Agency

Washington, DC 20300

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Characterization of Microwave Window Materials

Interim Report

May-October 1982

Introduction

Since February 1982, NBS has been engaged in a project concerned

with the properties of Boron Nitride. Hexagonal BN is a promising

candidate for use as a microwave window material. The window will reach

temperatures in the neighborhood of 3000 K for short periods of time.

It is therefore important to know the physical and chemical properties

of BN in this range. The focus of this project is on the electrical

d.c. conductivity of BN and on its dielectric behavior when subjected to

microwave radiation at very high temperatures.

The first four months (Jan. -April) have been used to explore

various experimental approaches to the measurement of the electrical

resistance and the temperature in the presence of large electrical and

thermal leaks. At the same time, computer programs were develooed to

calculate the dielectric parameters of BN in the low-GHz frequency

range.

Electrical Conductivity

Sample Configuration

Although hexagonal boron nitride possibly is the best electrical

insulator known up to 2000 °C, above this temperature the conductivity

-3 -1 -1 rapidly increases to values in excess of 10 ohm cm . This conduction probably is intrinsic in nature. In order to prevent degradation

and nonstoichiometry due to loss of nitrogen, which could cause large

extrinsic conduction, it is necessary to perform high temperature
- 2 -

measurements in nitrogen gas. According to the literature [1], the

equilibrium vapor pressure of ^

over BN is 0.1 atm at 2265 °C, 1.0 atm

at 2505 °C, and 3.0 atm at 2626 °C.

As stated in the first Progress Report (May 1982), above 2000 °C

one observes a leakage conductance--probably due to gas conduction--

which reaches values comparable to that of the BN sample. Consequently,

it is necessary to devise an experimental arrangement which avoids the

problem of the large leakage conduction path. One solution is a geometry in which the sample is isolated from the nitrogen gas (Scheme #1).

Another arrangement is a guard ring configuration whereby the sample and

sample leads are electrically shielded from the large 1 eak-currents to

ground (Scheme #2)

.

Scheme #1 '

For this approach, the insulation of the sample from the gas is

provided largely by boron nitride at a lower temperature, as shown in

Fig. 1. The actual BN sample is confined mainly to the volume between

the tungsten electrodes. This "sample" is part of a BN cylinder which

is positioned at the access opening of the lowest of the upper eight

heat shields. Above this level, the temperature drops rapidly. Consequently, the boron nitride cylinder above the top electrode has a high

resistance and contributes little to the conduction path. The bottom

tungsten electrode is held in place by a threaded BN plug. Due to this

geometry, it is difficult to translate the resistance, R, of the sample

into resistivity. However, a rough estimate indicates that the numerical value of the resistivity is of the order of 1 .5 R and certainly

does not exceed 2.0 R.
- 3 -

In the first run, the temperature of the sample was measured by a

W(3% Re) vs. W(25% Re) thermocouple attached to the top electrode. The

temperature in the center of the furnace was determined by means of a

W(5% Re) vs. W(26% Re) thermocouple introduced through the bottom of the

furnace and by means of a pyrometer sighted through a viewing port on

the side of the furnace. The readings of the pyrometer and of the

thermocouple in the center of the furnace agreed within 40-50 °C up to

2200 °C ; beyond this temperature, the latter was retracted from the

furnace.

The sample used in the first run was cut from a small block of high

purity boron nitride (HPBN-TS1 251 ; Union Carbide). The temperature at

the center of the furnace was raised to a maximum of 2480 °C, as indicated by the pyrometer. At this point, the sample temperature lagged

behind considerably: T = 1850 °C was the highest reading. All measurements were made with an ^

pressure of 1.0 atm. Results of this first

run are shown in Fig. 2.

In order to raise the sample temperature in the next run, the boron

nitride cylinder was made somewhat longer, such that the top electrode

was located 1.0 cm below the lowest horizontal heat shield. This made

it possible to reach a higher sample temperature of 2021 °C when the

maximum temperature in the center of the furnace was 2410 °C, as indicated by the pyrometer. Conductivity measurements were made at three

different pressures of the nitrogen gas: 1.0, 2.0, and 3.0 atm.

Results of this second run are also presented in Fig. 2.

Electrical measurements during the first run were terminated when

the tungsten wire failed between the sample and the BN insulator which
- 4 -

extended through the viewing port into the hot zone of the furnace (see

Fig. 1). An attempt to push the furnace temperature above 2500 °C

resulted in considerable effervescence and partial destruction of the

end of the BN insulator. The second run was terminated at a furnace

temperature of about 2500 °C when the wires of the lower thermocouple on

the sample broke.

Two materials failure modes are indicated by these results. The

first mode is the decomposition of BN at temperatures in excess of

2500 °C under a pressure of 1.0 atm of N£. This observation is in

agreement with the literature value of 2505 °C [1], No decomposition of

BN was evident, as expected, in the second run when the pressure was

increased to 3.0 atm of N

2

.

The second mode appears to occur through a reaction between the

tungsten wires and the BN parts. After each experiment, the BN sample

and insulators were inspected radiographical ly . Radiographs of sample

and insulators are shown in Fig. 3. The multiple breaks and balling up

of the tungsten wire suggest that the wire failed by forming a liquid

phase. This is in agreement with the W-B phase diagram [2]: l/^B^

melts at 2365 °C and excess boron lowers the melting temperature to

'v 2000 °C (Fig. 4). When the amount of tungsten exceeds the BN present

(W > 50 percent), the melting points of the W-B compounds and solid

solutions are 2600 °C or higher. Consequently, more massive pieces of

tungsten (rods and discs), in contact with BN, should not be subject to

disintegration if one keeps the temperature below ^ 2600 °C.

Scheme #2

In this arrangement (Fig. 5), the sample is located near the center

of the furnace suspended from a tungsten tube, which acts as an elec-
- 5 -

tr i cal shield. A "lip" at the bottom of this shield functions as the

guard ring. The sample is provided with two tungsten discs; these are

the electrodes for measuring the resistance of the BN sample. All these

parts are held together by two BN rings, threaded on the cylindrical

sample.

The sample resistance, R , is measured by means of an OP-AMP circuit [3]; R is deduced from the following expression:

X

where: R = sample resistance,

E. = applied voltage,

R^ = feedback resistance, and

E q

= output voltage.

The OP-AMP circuit plays the role of a very sensitive nulling

device (OP-AMP A). The circuit is strictly d.c.; OP-AMP's B and C are

filters to prevent any intrusion from low frequency a.c. sources.

The shield and the main furnace are at ground potential; point P,

between R and R f , is only a few microvolts above ground. Consequently,

no leakage can occur between the too lead to the sample and its surroundings. Possible leakage paths from the lower sample lead to the

grounded furnace body are not part of the main circuit (as long as Edoes not vary) and, hence, are not being measured.

Conductivity measurements on several BN and BN-contai ni ng samples

are in progress.
- 6 -

Theory of Microwave Window Transmission

1 . General Considerations

Under the conditions of atmospheric reentry, the ARV microwave

window material is subjected to most severe environmental conditions.

The very high outer surface temperature leads to ablation of the material and the flow of a heat pulse into the window. The temperatures

reached are sufficiently high that the thermal generation of conducting

carriers is sufficient to cause significant microwave absorption (and

reflectance) in many candidate materials. The processes induced by

reentry are so rapid that the temperature distribution and carrier

concentrations are nonuniform.

Complete modeling of the transmissivity of a microwave window would

require a knowledge of the ablation rate, the temperature profile, and

the enhancement of electrical conductivity at all times during the

reentry and also the effects of the external plasma of ionized gases.

In this part of the project, we address the more limited question of

finding the effects of the intrinsic conduction processes on the applicability of boron nitride for window use. We devote the principal effort

to the calculation of the microwave transmission through window material

at high temperatures, with a steep temperature gradient and with thermal

excitation of conductivity.

The calculations we perform are based on the model illustrated in

Fig. 6. Microwave radiation is incident from the left. Significant

reflection (to be calculated) occurs; the radiation in the window undergoes multiple internal reflections and a transmitted wave emerges,

propagating to the right. As the window ablates, the thickness of the
- 7 -

window decreases, leading to interference oscillations in the transmissivity. An additional complication is that, for the conductivities

and the microwave frequencies that are used, the electromagnetic skin

depth and the wavelength in the window are smaller than the thickness of

the hot layer at the outer surface. Thus, we must solve the problem of

electromagnetic radiation passing through a medium with parameters that

are changing slowly with respect to the wavelength in the medium.

Because of the immediate availability of suitable computer programs, we

felt that direct numerical calculation was the simplest way to treat

this problem correctly. Approximations utilizing the WKBJ [4] method

could have been used, but computer usage would probably have been

necessary anyway.

2 . Method of Calculation

The propagation of an electromagnetic wave in a medium having a

spatially varying electrical conductivity is described by Maxwell's

equations. If we assume that the material variation is a function of

one coordinate, z; i.e., that the medium is stratified and that the

radiation propagate is parallel to the z-di recti on, then the wave is

described by the pair of coupled linear differential equations:

dE _

cJz ‘ -ikzoH 3 (l.a)

-ike(z)E (l.b)

In the above, E and H are the electric and magnetic field intensities,

which are mutually perpendicular, and both are transverse to the z-
- 8 -

direction. Sinusoidal monochromatic fields of angular frequency, w, are

assumed; the convention for the time variation is by use of the underwave vector equal to the reciprocal wavelength times 2 tt. The complex

dielectric constant, e, is given by,

where e Q

is the permittivity of free space, < e is the relative dielectric permittivity of the window material, and o(z) is the spatially

varying electrical conductivity.

In the above, SI units are used exclusively. The numerical solutions of Eqs. (1 .a) and (l.b), subject to specially imposed boundary

conditions, enable one to compute the characteristic matrix of the

material. By using standard methods [5], which we shall not reproduce

here, the transmissivity and reflectivity of material of arbitrary

dielectric profile can be obtained once the characteristic matrix is

computed.

The problem is thus completely specified if we give the temperature

profile and the dependence of conductivity on temperature. For the

temperature profile, we use the values reported by the TRW Corporation [6] on data for hot pressed boron nitride. The profile is given

approximately by the exponential form,

stood factor, e~

lujt

. Z

Q

is the impedance of free space, and k is the

e ( z ) = £ 0

< e + ia(z)/u) ( 2 )

( 3 )
- 9 -

where a = 0.216 cm""* is the decay constant and T

q

is the surface temperature. For the conductivity of BN, we use the loss tangent data compiled by Hathaway et al . [7]. The loss tangent, tan a, is related to

the conductivity by,

tan a = . (4)

e k w

o e

Here, is the dielectric constant of BN, taken as 3.1. Their data [7]

are fitted well by the Arrhenius form,

a(T) = c

o e"

A//kT

, (5)

3 -1 -1

where the prefactor, a

Q

= 1.63 X 10 o, cm , and A = 3.08 eV, are

consistent with a band gap of 6.0 eV. For a surface temperature of

3150 K, the conductivity at the surface would be 2.0 ft”"* cm~^ ; very

close to the values extrapolated from the measurements of this report

(see Fig. 2)

.

3. Results of the Calculations and Discussion

In Fig. 7 through Fig. 10, we show the calculated transmissivities

of boron nitride windows as a function of thickness for a range of

surface temperatures. The curves have common characteristics which we

now shall describe. The transmissivity falls very rapidly as window

thickness increases from zero. The curves all show that the principal

effects of the conduction processes occur in the outer one or two millimeters of the hot face. All curves show a near-sinusoidal oscillation

with thickness, which is characteristic of the multiple internal reflec-
- 10 -

tions that occur in the cool part of the window. The percent transmissivity increases as the surface temperature is reduced, to as high as

nine percent for T

q

= 2850 K.

In the various cases studied, the reflectivity varied from 80 percent to 85 percent, and the absorptivity varied from 10 percent to

15 percent. This demonstrates the mirror-like properties of the outer

hot surface of the window.

The oscillatory dependence upon thickness suggests that one could

observe, at 10 GHz, a series of transmissivity peaks as the ablation

process proceeds. We consider the peak values as the maximum obtainable

transmissions, for if the window were coupled to a continuously tuned

cavity the interference cancellation could be removed.

The conclusion to be drawn from these calculations is that, at the

considered reentry conditions, the transmissivity of intrinsic boron

nitride windows at 10 GHz will have an upper limit of 10 percent;

i.e., the one-way loss will be 10 dB or greater. Some improvement could

be obtained by altering the material composition and form in such a way

as to reduce the surface temperature or to increase the temperature

gradient. Calculations of this type should be extended to materials,

such as woven BN-SiC^ fiber composites and other candidate materials.

Also, an improved theory of the temperature profile should be developed.
1 .

- 11 -

References

Gmelin Handbuch der Anorg. Chemie, Band 13: Borverbindungen

,

Teil 1; Springer Verlag, Berlin-New York, 1974, p. 70.

2. "Compendium of Phase Diagram Data", E. Rudy, AFML-TR-65-2 , Part V,

Air Force Matls. Lab., WPAFB, Dayton, OH, 1969.

3. "Operational Amplifiers", J. G. Graeme, G. E. Tobey, and

L. P. Huelsman, McGraw-Hill Book Co., New York, 1971.

4. "Light Reflection From Films of Continuously Varying Refractive

Index", J. Jacobsson, Progress in Optics , E. Wolf, Ed., North

Holland, Amsterdam, 1966; Vol . V.

5. "Principles of Optics", M. Born and E. Wolf, Pergamon Press,

Oxford, 1965; pp. 51-66.

6. "The Prediction and Measure of Dielectric Properties and RF Transmission Through Ablating BN Antenna Windows", K. Golden (TRW),

B. Hanawalt (AVCO), and W. Ossmann (AVCO) , AIAA-81 -1085 , 16th

Thermophysics Conf . , Palo Alto, CA, 1981.

7. "Microwave Loss at High Temperatures in Radome Materials",

K. Hathaway, J. Cullen, and A. A. Campol attaro , Nav. Surf. Weapons

Ctr., TR-80-555 , April 1981.
- 12 -

Figure Captions

1. Boron Nitride sample with internal electrodes (Scheme 1):

A,B--tungsten electrodes

T--W(3Re) vs. W(25Re) thermocouple

H--heater

S--radiation shields

2. Resistance of BN as a function of reciprocal temperature:

o —Run I

x--Run II; P M =1.0 atm

in 2 o--Run II; P M =3.0 atm

n

2 Radiographs of BN sample.

Phase Diagram of W-B system.

5. Schematic of sample holder, furnace, and OP-AMP circuit (Scheme 2).

6. Illustration of the model for calculating the microwave transmissivity of BN windows.

7. Calculated transmissivity of BN microwave windows as a function of

thickness for 1.0 GHz radiation and a surface temperature of 3150 K

(2877 °C).

8. Calculated transmissivity of BN microwave windows as a function of

thickness for f = 10.0 GHz and T = 3150 K (2877 °C)

.

9. Calculated transmissivity of BN microwave windows as a function of

thickness for f = 10.0 GHz and T = 3000 K (2727 °C)

.

Calculated transmissivity of BN microwave windows as a function of

thickness for f = 10.0 GHz and T = 2850 K (2577 °C)

.

10 .
FIGURE 1

BORON NITRIDE SAMPLE WITH

INTERNAL ELECTRODES
FIGURE z

RESISTANCE OF BN vs

RECIPROCAL TEMPERATURE

3333K 2000K 1429K

104/T(K)
FIGURE 3

RADIOGRAPHS OF BN SAMPLE

(A) BEFORE HEATING

(B) AFTER HEATING
3400

3200

3000

2800

2600

2400

2200

2000

1800

FIGURE 4

iASE DIAGRAM OF W-B SYSTEM
SCHEMATIC

OF

SAMPLE

HOLDER,

FURNACE,

AND

OP-AMP

CIRCUIT

co
FIGURE 6 O Ml

tsi 5

CO gi < 

pcscc o o < f t

cc

LU

HiO<

LiCC

</)

GRADED

CONDUCTIVITY

PROFILE
%

TRANSMISSIVITY

FIGURE 7

CALCULATED TRANSMISSIVITY OF

BORON NITRIDE MICROWAVE WINDOWS
FIGURE

8

CALCULATED

TRANSMISSIVITY

OF

BORON

NITRIDE

MICROWAVE

WINDOWS

CM

O

<3

-

O

CO

o

cm

CO

o

CO

o o

CM

o

o

o

AllAISSIWSNVai %

I

!

WINDOW

THICKNESS

(cm)
CALCULATED

TRANSMISSIVITY

OF

BORON

NITRIDE

MICROWAVE

WINDOWS

CO

CM

o

A1IAISSIIAISNVU1 %

WINDOW

THICKNESS

(cm)
FIGURE

10

CALCULATED

TRANSMISSIVITY

OF

BORON

NITRIDE

MICROWAVE

WINDOWS

O

N

I

CD

>

O

o

LU

CC

LL

XL

O

IT)

CO

CN4

II

O

cvi

o o

CO

o o

CO CM

CO

o

o

A1IAISSIIAISNVU1 %

WINDOW

THICKNESS

(cm)
NBS-114A (rev. 2-8C) U.S. DEPT. OF COMM. O MM. BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

SHEET (See instructions) NBSIR 83-2646 January 1983

4. TITLE AND SUBTITLE

"Characterization of ARV Antenna Window Material"

(Progress Report No. 2. October 1982; Defense Nuclear Agency)

5. AUTHOR(S)

H. P. R. Prederikse, A. L. Dragoo. A. H. Kahn, and W. R. Hosier

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10. SUPPLEMENTARY NOTES

|

. Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gn i fi cant bibliography or literature survey, mention it here)

Boron nitride is a major candidate for use as a microwave window material. To assess its feasibility for this purpose, it is essential to know the electrical

and dielectric properties at high temperatures. This report discusses the experimental approach to electrical conductivity measurements above 1800 °C and presents

some initial results. At the same time, computer calculations have been performed

which have yielded values of the reflectivity, absorption, and transmission of

boron nitride in the temperature range 2500-3000 °C.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s)

Boron nitride; Calculated transmissivity; Electrical conductivity; High temperatures;

Microwave radiation

13. AVAILABILITY 14. NO. OF

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