v*<*

NATIONAL BUREAU OF STANDARDS REPORT

7835

THERMAL CONDUCTIVITY REFERENCE STANDARDS

Complementary Report

March 1963

H, E. Robinson

to the

Bureau of Ships

Department of the Navy

Washington, D, C,

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT

1006-20-10461 March 25, 1963

NBS REPORT

7835

THERMAL CONDUCTIVITY REFERENCE STANDARDS

H„ E„ Robinson

Heat Transfer Section

Building Research Division

Complementary Report to the

Bureau of Ships

Department of the Navy

Washington, D„ C 0 INDEX NO, S-R007 12 01, Task No, 800

(BuShips 17003-716-62) „ Code 2781

by

IMPORTANT NOTICE NATIONAL 3UREAU OF S

for use within the Government, and revie v. For this reason, t vnoie or in part, is not authi Bureau of Standards, Washing

the Report has been speciticall

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

iss accounting documents intended

subjected to additional evaluation

; listing of this Report, Pithvr : ~

e Office of the Oi*scto r

, Nation;.!

i the Government agency for wMen

copies for its own u?e.

I). S. DEPARTMENT OF COMMERCE

NATIONAL OUREAU OF STANDARDS
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THERMAL CONDUCTIVITY REFERENCE STANDARDS

TABLE OF. CONTENTS

PAGE

ABSTRACT .

' 1

1. INTRODUCTION • 1

2. A CUT-BAR APPARATUS FOR CALIBRATION USING REFERENCE STANDARDS... 3 i

3. CALIBRATION AND USE OF THE APPARATUS 9

4. SELECTION OF METER BARS .. 11

5. . TYPES OF MATERIALS FOR THERMAL CONDUCTIVITY REFERENCE STANDARDS. 12

1. Materials not sufficiently uniform to forgo need for

measuring each reference specimen 14

2. . Stocked materials of proven uniformity: batch samples 14

3 . Materials of high purity. 14

6. PROPERTIES OR ATTRIBUTES DESIRABLE FOR REFERENCE STANDARDS 15

LIST OF FIGURES

Figure 1« Schematic arrangement of a guarded cut-bar apparatus

for comparative determination of thermal conductivity 9 showing the bar assembly (me ter- specimen-meter) within

a concentric guard cylinder. -Steady temperatures at

the indicated longitudinal positions of the bar

assembly and guard are V and 0 s and T and R,

2

TABLE OF CONTENTS (Coat’d)

J,i iit :> /: Figure 4 (Cone *d) :

PAGE

Figure 2„ Left diagram Illustrates temperature distribution in a cut-bar comparative apparatus along the mater-specimenmeter assembly (dashed line) and along a linear guard

matched at ends (solid line)* Eight diagram shows

change in longitudinal heat flux in bar assembly with

. position* for (M) a matched guard* (L) a linear guard

matched at ends* (L^) a linear guard G o 01\T cool at

ends* » 4'

Figure 3* Geomat rieal factor as a function of the ratio of guard

end specimen diameters* for four - types of guarding:

(M) matched guard* (L) linear guard matched at ends*

(I) Isothermal guard at specimen mean temperature (Ipj)

. isothermal guard almost wholly at mean temperature of

specimen $ but matched at ends . « a » • «•«»«. . *

.

6

figure 4* Schematic for a guarded cut-bar apparatus designed for

calibration of meters by means of thermal conductivity

reference specimens % with the calibration substantially

independent of precise guard temperature management*, •« * *„ * 8

i re 5 S Conductivity factor for cut-bar apparatus as a function

of specimen thermal resistivity (1/KS )* for three

different meter bars at temperatures of 0? and 1G0G*C«»««« Ip

THERMAL CONDUCTIVITY REFERENCE STANDARDS

Complementary Report

March 1963

by H. E. Robinson

ABSTRACT

As a preliminary step to discussion of thermal conductivity reference

standards, seme results of a mathematical analysis of longitudinal heat

flow in a cut-bar apparatus (meter-specimen-meter) are presented graphically. The results lead to the conclusion that a guarded cut-bar apparatus is possible in which the heat flowing longitudinally in the centrallylocated specimen is a fixed proportion of that flowing in the meters,

which proportion depends only on a factor involving the conductivities of

the specimen, the meters, and the surrounding powder insulation, and does

not depend upon precise management of the guard temperatures. Such an

apparatus is shown schematically, and a method of calibrating the meters

of the apparatus by using a reference specimen of known thermal conductivity in place of the test specimen is described, with procedure and

equations for its calibration and use. Information is given graphically

on the variation of the conductivity factor with the conductivities of

the specimen and the meters. Finally, the necessary or desirable properties and attributes of materials for use as thermal conductivity references

are discussed.

This report is a slightly modified version of a paper given by the

author at the informal Second Conference on Thermal Conductivity, held

at the National Research Council, Ottawa, Canada, on October 10-12, 1962.

Since its contents relate to and complement, from an application point of

view, an undertaking sponsored by the Bureau of Ships, Department of the

Navy (Bu Ships 1700 S-716-62) for development of a specific thermal conductivity reference material, the paper is being made available as a complementary report to the sponsor.

In an earlier NBS Report^, reference was made to the use of thermal

conductivity reference standards as a means of facilitating and improving

the accuracy of thermal conductivity measurements. It was pointed out

that such standards are best used in the role of substitute specimens,

that close duplication of the accessory conditions of the apparatus is

1/ NBS Report 73^7 "Thermal Conductivity of Semiconductive Solids} Method

for Steady^State Measurements on Small Disk Reference Samples, Technical Progress Report for Period July 1 to September 30 » 1961," Nov* 14,

1961, pp 4-5 asad

1. INTRODUCTION
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FIGURE 1. SCHEMATIC ARRANGEMENT OF A GUARDED CUT -BAR'

APPARATUS FOR COMPARATIVE DETERMINATION OF

THERMAL CONDUCTIVITY 9 SHOWING THE BAR ASSEMBLY

(METER- SPECIMEN -METER) WITHIN A CONCENTRIC

'• GUARD CYLINDER, . STEADY TEMPERATURES AT THE

. INDICATED LONGITUDINAL POSITIONS OF THE BAR'

ASSEMBLY AND GUARD -ARE V AND -0, AND T AND R s RESPECTIVELY. /

essential to conserve the accuracy of the calibration of the test apparatus, and that therefore the design of the test apparatus is important as regards the precision with which the accessory conditions can be controlled

and duplicated*

As a preliminary . step to consideration of materials for reference

standards, and to focus some attention on their uses and therefore on the

attributes they should have, this report first presents a development of

the ideas mentioned above, leading to a schematic design for a cut-bar

comparative - i.e. , calibrated - apparatus for measuring the thermal conductivity of small specimens, and to the procedure for its calibration and

use. The apparatus that emerges from the development appears in prospect

to be simple to build and use, and yet to be capable of satisfying the

requirements indicated in the first paragraph.

2. A CUT-BAR APPARATUS PGR CALIBRATION

USING REFERENCE STANDARDS

In the earlier report mentioned, a general mathematical solution was

given by B. R. Flynn for calculating the heat flux at various longitudinal

positions along a cut-bar apparatus assembly (meter- specimen-meter arrangement as shown in Figure 1) , and the solution was developed and shown

graphically for the case of matched guarding. It is sufficient for present

purposes to take from the general solution the following information:

a) If the conductivity of the specimen differs from that of the

meter bars, there is an interchange of heat between the bar assembly and

the surrounding powder insulation in the vicinity of the specimen, even

with perfectly matched guarding. This leads to a change in longitudinal

heat flux in the bar assembly in the vicinity of the specimen. For the

case of matched guarding, the net change of heat flux in the bar assembly, from a selected position or origin to a particular position is proportional to the product of a conductivity factor (Fic ) , which depends

only on the conductivities of the specimen s the meters and the powder

insulation, and a geometrical factor (Fg) which depends only on the dimensions of the bar assembly and the guard.

b) If the temperature of the guard varies linearly with longitudinal

position from end to end, the change in bar assembly heat flux with position is equal to the product of the same factor 1A. as in a) and a modified geometrical factor (F£) which takes into account also the integrated

radial heat interchange between the bar assembly and guards if the guard

matches the bar assembly in temperature at the origin and at an equal

distance on the other side of the specimen. If the guard temperatures at

these positions do not match those of the bar assembly, an additional term

involving the temperature differences must be added.

TEMPERATURE

, v

/V

-4-

SPEC1MEN LENGTH _ , Q

SPECIMEN DIAMETER

' GUARD DIAMETER _, Q

SPECIMEN DIAMETER

Ks — Kj

=0.5, =0.01 , F = -0.01

FIGURE 2. LEFT DIAGRAM ILLUSTRATES TEMPERATURE DISTRIBUTION

IN A CUT -BAR COMPARATIVE APPARATUS ALONG THE

METER-SPEC IMSN -METER ASSEMBLY (DASHED LINE) AND

ALONG A LINEAR GUARD MATCHED AT ENDS (SOLID LINE)

„

RIGHT DIAGRAM SHOWS CHANGE IN LONGITUDINAL HEAT

FLUX IN BAR ASSEMBLY WITH POSITION, FOR (M) A

MATCHED GUARD, (L) A LINEAR GUARD MATCHED AT ENDS,

(LD) A LINEAR GUARD O.OiV COOL AT ENDS

These observations are illustrated in Figure 2. The schematic bar

assembly considered has the specimen and meter bars of equal length (w/3) , equal to their diameter ( 2a) , which is one-third of the guard diameter*

Such dimensions seem practical for many applications, and were selected

to avoid excessive effects cue to integrated radial heat exchange with the

guard. The bar assembly has the temperatures V and zero at its two ends;

the corresponding guard temperatures are T and R. In the diagram at the

left, the dashed line represents the • idealized temperature along the bar

assembly, assuming unchanging longitudinal heat flux, and the solid line

a linear guard matched at the ends (that is, with T - V, and R = 0). If

a matched guard were used, its temperature would be given by the dashed

line. If a guard isothermal at the mean temperature of the specimen were

used, T - R - V/2.

The diagram at the right of Figure 2 shows the change in longitudinal

heat flux in the bar assembly, versus distance from the hotter end of the

hotter meter, for matched guarding (M) , for a linear guard matched at the

ends (L) , and for a linear guard with its temperatures at the ends 0.01V

cooler than these of the bar assembly (L]))« (The case for an isothermal

guard, with T « R = V/2, cannot be shown well on this diagram. The power

change (7 ) at z/w ~ 0,5 is -lp, 9 percent.)

The power change curves show that if the specimen and guard tempera

tares have polar symmetry, about a point at the center of the specimen,

the indications of heat flow by the two meters will be equal. If they

are polarly asymmetrical, as in t

one percent , the two meters will

indications of the maters do not

the specimen if the conductivity

ductivity (Ks ) of the specimen- do

he case of the linear guard displaced

disagree. However, in both cases, the

correspond to the actual heat flow through

factor is not zero, i.e., if the cones not equal that of the meters (Km)

.

in

guard \j

a

case of

ciature

Figure 2 , the fractional power change 7 for the case of a matched

.s- calculated using equation (28) of D. R„ Flynn ! s paper. For the

a' linear guard, his general equation (18) yields, in -the nomenof this paper.

7(a) 1 •V"5a K,

n=X

„ /njta.nrtb. _ gir_rt_r)

i ^ ,n3fca. nrtb x j 1 - w

_nitz

w

. n:rci nit

Sin-rr*-*COS~-

2w 2

1 . Ki 2w(T-V)z + (R-fV-T) z2

•J* ?>»» £ * ..

\

mtrr m Wti r r. , .1. —

n

I a‘

£iwin b/a

( 1 )

GEOMETRICAL

FACTOR

GUARD DIAM pt 5 ft f\ f\ U i iJi

FIGURE 3. GEOMETRICAL FACTOR AS A FUNCTION OF THE RATIO OF

GUARD AND SPECIMEN DIAMETERS , FOR FOUR TYPES OF

GUARDING: (M) MATCHED GUARD , (L) LINEAR GUARD

MATCHED AT ENDS, (I) ISOTHERMAL GUARD AT SPECIMEN

MEAN TEMPERATURE , (%) .ISOTHERMAL GUARD ALMOST ' WHOLLY AT MEAN TEMPERATURE OF SPECIMEN, BUT

MATCHED AT ENDS

7

This equation (and equation (28)) involved in its development the assumption that Ks S

g = KjjjSjqj rather than the truer relation that

KsS s = 7 (z=w/2)

where S 3 and Sm are the longitudinal temperature gradients in the specimen

and meter bars * respectively. For tolerable values of 7, the error in y

due to this assumption is of secondary importance.

For a linear guard matched in temperature at z = 0 and z = w, the

second term of y(z) equals zero, and

, v — / 1 Is 8w

7<z) = *<—-—> * -gnrta mtb

X

n

n^ ~ / n£ta f nJtbv

“oC

, i»fzl . niti nit

i - cos——— sin——cos

w j 2w 2

( 2)

or 7(2) - Pi F'' X S (2a)

Figure 3 shows values of the geometrical factor at 2 = w/2, for various

ratios of guard diameter to specimen diameter for the case of a specimen

(and meters) of length equal to their diameter, for four types of guarding.

Curve M is for a matched guard* curve L for a linear guard matched at the

ends* e ."/e 1 for an isothermal guard with its ends at the mean temperature

of the specimen* and curve Iiq for a guard isothermal at the specimen mean

temperature ever the length 0.0 Iw to 0. 99w, but changing linearly in the

length O.Olw to match the temperatures at the ends of the bar assembly.

Of major interest is the fact that for three types of guarding (M,L,

Iv) * the geometrical factors practically coincide at a value of 2.93 for

guard diameters greater than about seven specimen diameters. Thus, for

these cases, the power change fraction 7 is equal to 2.93 F> , if the diameter ratio is seven or greater* and the precise management of the temperatures of the guard is immaterial, provided that its mean temperature

is substantially equal to the mean temperature of the bar assembly. All

three of these cases are characterized by the condition that the virtual

plane surfaces 2 — 0 and 2 » u in the insulation between the bar and guard

are isothermal at the corresponding temperature of the bar assembly. (In

the case of curve I* the temperature of these virtual plane surfaces is a function of the- logarithm of. the radius.) In short, the geometrical factor
....

.

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THRUST

FIGURE 4. SCHEMATIC FOR A GUARDED CUT-BAR APPARATU.S DESIGNED

FOR CALIBRATION OF METERS BY MEANS OF THERMAL

CONDUCTIVITY REFERENCE SPECIMENS, WITH THE

CALIBRATION SUBSTANTIALLY INDEPENDENT OF PRECISE

GUARD TEMPERATURE MANAGEMENT

attains a unique and constant value when the ends of the insulation between

the bar assembly and the guard are isothermal at the corresponding temperatures of the bar assembly * and the guard diameter is large enough*

The apparatus shown schematically in Figure 4 is designed to satisfy

the conditions developed above* Thick disks of conductive' material of

radius b « 7a, approximately* are used to provide substantially isothermal

surfaces at 2 = 0 and z » w; the guard is a suitable thin-walled cylinder

of internal radius slightly larger than the disk radius* positioned cn

poorly-conducting supports carried by the lower disk* • A guard so arranged

might possibly attain the mean temperature of the tv© disks; if necessary,

electrical heating of the guard could he used to establish the desired mean

temperature* The heaters cn the disks* indicated schematically* establish

their temperatures and provide the heat flowing longitudinally between them.

For very high temperature operation the total assembly probably should be

placed within an enclosing furnace*

3* CALIBRATION AMD USE 037 THE APPARATUS

Assume that an apparatus of the kind* and geometry, shown in Figure

4 has been constructed* with thermocouples installed as indicated by the

solid circles* . The position normally occupied by a specimen is occupied

by a reference specimen of known thermal conductivity (ICr) * with which the

apparatus (i*c** the installed meter-bars* or meters) are to be calibrated.

Assume that the upper disk has been brought to a steady temperature

suitably higher than that of the lower disk and that the average of the

temperatures of the two guard thermocouples approximates the average of

the temperatures • of the two specimen thermocouples* Under these conditions* measurements are made to ascertain Sr and Wnr , the temperature

gradient in the reference specimen s and the average of the temperature

gradients in the two meters* respectively* With these data* one can write

- **%Sr

'

in which the subscript r refers to values pertinent with the reference

specimen in place* and (l+yr) is the fractional power flowing in the bar

assembly at the position of the mid-plane of the reference specimen*

Similarly* in a similar test conducted with a test specimen (subscript

s) - in place in the bar assembly* one can write

A

w.s b

rm ^ lv?

s

J “ ~xs^

s

- 10-

Xf in both tests the average values, of the temperatures of the two meters

were the same (or If the meters do not change significantly in conductivity

with temperature) , Kmr and IC^g will be equal and these two equations then

yield the relation

-is *£ms S r i+7 g

K-r Syn-f Sg 1+7r

(3)

It has been shown that for the assumed apparatus

7(2 - f) - 2.93Fk = 2.93Ki (—• - ~—

)

m ^spec

Accordingly.

1 + 7a

1 + 7r

1 + 2. 95Kl (r

Saa.

1 + 2-9JIC, fe— - &

This is awkward to evaluate } since KX, (K^g will here be assumed equal to

.IX,,.) may not be accurately known. However , (l+7 s )/(l+7r) may be approximated by l+7s-7r> with a fractional error equal to 7r (7 s “*7-r)/(l+7 s ) • Within the uncertainty with which and may be duplicated in the use

of the apparatus, and the fractional error involved in the above approximation, one can use the approximation and avoid needing to know Km. Thus

equation 0) becomes

<JX & _ t ^ms j^r

K.r " Snir /S

s (l+7s-7r) 1 + 2.93-1(1 - Kr

Kr, K

' (4)

wherein ICs /K-r is ascertained by a few repetitive calculations using improved values of ICr/Ks in the bracketted tern.

Some obvious precautions or arrangements desirable in the use of the

envisaged apparatus include the following t

a) The powder insulation of conductivity Kg should be installed, and

if necessary renewed from a uniform stock, so that li± is substantially the

same in all tests at the same temperatures «,

b) Contacting surfaces of the meter bars and specimens should be

clean and quite flat to avoid perturbations of the calibration and tests

due to altered thermal resistance at contacts*

c) The reference specimen and. the test specimens should always have

the same dimensions, quite closely* Thermocouples should be attached in

both by the same method, and should be equidistant from the mid-plane of

the specimen, with the separation the same for all specimens.

4. SELECTION OF METER BARS

A cut-bar apparatus of the kind envisaged, if calibrated and used ac- cording to the procedure described, should be capable of good accuracy over

a wide range of specimen conductivities „ However, for precision of observations, it is desirable that the temperature differences measured in the

specimen and the meters be of approximately the same magnitude.

As a guide in selecting suitable meter bars for particular measurements, and as a means of estimating the range of specimen conductivities

most appropriate for measurement with particular meter bars. Figure 5 presents negative values of the conductivity factor Fk (in percent) versus

the reciprocal of the specimen conductivity (specimen thermal resistivity),

for three different meter bar materials: Armco iron, Pyroceram 9606, and

fused silica. Two straight lines are shewn on Figure 5 -for each meter

material, one corresponding to its use at Q^C, and the other to its use at

1000*0 (the 1000 °C line for fused silica is hypothetical, assuming that it

is, or can be made, opaque to thermal radiation). The conductivity factors

are predicated on pure fine alumina powder insulation having the conductivities given on Figure 5, and intermediate values which vary substantially

linearly with temperature* The values of thermal resistivity used for the

meter bar materials are indicated by the value of 1/KS at the intersection

of the meter bar line with the zero value line for the conductivity factor.

It may be of interest to note that the product of the negative percentage conductivity factor and the geometrical factor for a cut-bar apparatus (the latter could easily have values as large as 3 or more) indicates • the percent error in the obtained conductivity of the specimen, if the

latter were to be calculated simply on the basis of the heat flow indicated

by the meters * For example # with an Armco iron meter at 0°C, the negative

conductivity factor for a specimen of 0.025 conductivity (1/KS - 40) is

about 4 percent, and with a geometrical factor of 3 the error of the uncorrected conductivity would be about 12 percent.

l

7 igure 5 shows that , as might be anticipated, the negative conductivity factor, and therefore the error in conductivity, is relatively, small

for Armco iron maters, for specimens of resistivity 10 cm deg C/watt and

less. For Pyroceram 9606 meters, the values are relatively small at G°C

for specimens of resistivity between 10 and 50, and at 1COO C C, for spaelraans of resistivity between JG and 50 • Similar observations can be made

for fused silica meter bars, which at O'X seem well suited for measurements of specimens of resistivity between 60 and 100 cm deg C/watt. (The

line for a hypofchetically-opaque fused silica at 1000 ''G should not be construed as realistic^ rather, it sets a goal for such a material.)

The light dashed lines labeled “Inconel 702 specimen" and "fused silica

specimen" (again hypothetical) indicate how the conductivity factor for

these specimens, tested with Pyroceram 9506 meters, would vary as the mean

temperature of the test increased from 0°C to 1CG0 C C.

I

5. TYPES OF MATERIALS FOR THERMAL CONDUCTIVITY REFERENCE STANDARDS

One can imagine one of p. W. Bridgman's aboriginal Bushmen setting up

a system of thermal conductivity reference specimens on the basis of a series

of solids of different colors or weights, or other qualities. The interesting thought is that if he hud only one standard, and it (and each other

solid) was stable in conductivity, an effective aboriginal thermal conductivity regime would exists However, trouble could be anticipated if he

attempted to have two basic standards in this regime. Perhaps, after much

confer ion, Iridgman's Buslmtin would conclude that stability was the important desideratum for a regime, and that (in our terms) absolute thermal

conductivity was really secondary, if not actually a nuisance.

This vignette contains much truth, but for us not all of it. Modem

man requires absolute values of conductivity, to fit into his broad system

of physics,- and for applications ranging from submarines to space vehicles.

The uncertainties in hie absolute values of conductivity depend, of course,,

on the state of the art. Obviously, it is important to reduce them as much

as feasible to promote concordances of .conductivity values, one with another,

and with related other properties of the materials. Nevertheless, it remains true that stability of conductivity, and. uniformity, are prime requirements for thermal conductivity reference standards - so much so that it is

logical to classify possible materials for standards in categories based on

these qualities aa follows:

"A

001

-13-

FIGURE 5. DNDUCTIVITY FACTOR FOR CUT -BAR APPARATUS AS A

[TNCTION OF SPECIMEN THERMAL RESISTIVITY (1/Kg),

DR THREE DIFFERENT METER BARS AT TEMPERATURES

F 0° AND 1000°C

>14*

1* Materials not sufficiently uniform to forgo need for measuring each

reference specimen

Such materials often must be need because there is no better alternative material* An example is the semi-rigid, fiber-glass insulating board

furnished by KBS for checking ASTM. G177 hot plate equipment, or calibrating

comparative apparatus for measuring the thermal conductivity of good thermal

insulators* Again, an experimenter may use a particular material as a heat

flow meter, and later may require the best possible value for its thermal

conductivity*. The fault in such materials is their need for individual

measurement, which is uneconomic j they may be excellent in all other important respects, including stability under well-defined conditions*

2 * Stocked materials of proven uniformity; batch samples

These are materials known , or found, to be quite uniform in thermal

conductivity within a batch or lot, so that measurements made on a relatively few samples of it are sufficient to define the conductivity of the

entire batch* Considerable exploratory work may be needed to assure that

u material is satisfactory for this purpose, but if the batch (and the deuand) is large enough, the cost per specimen may be quite moderate* Batch

operations have the advantages that often the material can be given properties peculiarly suitable for the proposed use by compounding, doctoring,

or special specification, that it may be possible to furnish specimens in

a variety of shapes or sisses, and that generally the custodian of the stock

becomes known as a source from which specimens can readily be obtained.

It is evident that batch materials are likely to be compounds or mixtures of elements, selected in part because they have conductivities appropriate for reference use for particular purposes, and perhaps other desirable properties obtained by doctoring*

b * Materials of high purity

Chemical elements of high purity are expected to have unique thermal

conductivities * as well as other properties, which may be defined as their

limiting values ns impurities are reduced* Single- crystal materials can

be regarded in a similar, way* Thermal conductivity reference materials of

'

tkla kind are attractive iii that once the conductivity of the pure material Lai. been adequately determined , reference specimens could- be obtained

from any scarce capable • of supplying material of adequate purity* Relatively sisipla measurements may suffice in some instances to determine the

.decree .of purity* For example 9 the purity of platinum is readily ascertained by the ratio &£ its electrical resistance at 100 to that at 0°C,

In considering pure .elemental materials , however, it must be recognized that at present the thermal conductivities of almost none have been

measured and confirmed or cross-checked^ over a wide range of temperatures 3 to the accuracy probably possible to the current state of the art. Further

their stability may be questionable because highly pure elements are quite

reactive chemically, and protecting -hen from adverse contamination during

use a especially at high temperatures, may be difficult, even in inert atmospheres or in a vacuum*

im assessment, in general, of the comparative merits of batch materials versus high-purity materials as reference standards cannot, of course

be conclusive® An important point, however, is that the electrical conductivity * and therefore presumably the thermal conductivity, of ultra-pure

elements is usually markedly affected by the first traces of impurity, at

least at low and moderate temperatures* On the other hand, the conductivities of multicomponent materials (sometimes delicately referred to as

*' garbaged- up

3 *) are often relatively insensitive to moderate variation in

composition, although there may arise a greater sensitivity to thermal

history or heat treatment, or to phase transformations in the range of

working temperatures » It is also pertinent that few usable pure elements

have thermal conductivities in the range in which reference specimens appear currently mat needed, that Is, below about 0*1 watt/cm C* An argument in favor of pure materials is that many are used and are available

m ;r as references in other respects, such as chemical, spectroscopic, and

freezing-point standard samples*

6® PROPERTIES Oh ATTiaBUTES DESIRABLE FOR REFERENCE STANDARDS

In addition- to the qualities already discussed, of appropriate, s tablej. and uniform thermal conductivity, a number of other attributes are

desirable for reference standards* It is not essential that a reference

standard be. usable over a wide range c-f temperature, but it is desirable*

Consequently, the remarks as to desirable properties below are meant to

connote that adherence to the quality over a wide range of temperature is

also, and in itself, desirable®

In most cases rigid and hard materials, capable of being finished no and retaining polished surfaces, are preferable* Materials easily subject

to strain or surface work-hardening which cannot be largely relieved, or

having large or anisotropic thermal expansion coefficients, or Poisson 8 s rati© values^' or which have significant rheological characteristics, are

less desirable* Hygroscopic or highly sorptive materials may, of course,

not he suitable for some purposes*

Silica t herutoccup lea must & Ireat always be used with reference spedmans . the physical properties of the material which might affect , for

example, setting a thermocouple in a groove must.be considered , as wall -as chemical reactions which eight contaminate the thermocouple* Electrical

insulation of the thermocouples it much simpler, and their use is therefore more precise, if. the material .is substantially non- conducting

electrically*

Very s'hbsteittlal opacity to thermal radiant energy appears essential,

'

.a requirement that may sariouely restrict the usefulness of tingle-crystal

materials * Other not adequately opaque materials may be capable of being

made more opaque by doctoring*

Resistance to chemical inter-reactions with other materials which

might affect the conductivity of either is, of course, required, and an

eusociated question is that of vapor pressure at elevated temperatures*

M&teri&lc that do not require a protective atmosphere or uoa of a vacuum

may be preferable* not* merely because of convenience, but because 'die conductivity of 'the reference* or ether critical parts of the testing apparatus, especially if there are porosities, may be altered by these conditions*

Xa some instances, references for use in special atmospheres may be needed*

Materials nut having transformations affecting their thermal conductivity in the working tempeta tare range are, of court a* much to be preferred

ever those which have them* However, in the latter cases, it may be possible, by suitable heat treatment, or doctoring, to put a material in the

condl eion of eua extrema or the 'other of the transformation , and thus

reader it stable over a wide temperature range*

A further desirable quality of a tl conductivity reference material is that it have a specific . ...... not >ject to discontinuities of

slop©* Such materials would bo factory alee for uae ee thermal diffusivity references, for which there my be a need paralleling that forconductivity references*

Xf thin survey end listing, or desirable or undesirable attributes of

e.^mi conductivity reference simudL rd materials were to be rede more complete or detailed, it would undoubtedly be even more formidable* hertunately, it la rare of a check Hat then a bill of particulars, and in

many iroe

ic&& 1fee force or impact can be softened or avoided by limiting

the working temperature • range for a material*

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