Density of columnar-grained ice made in a laboratory

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Density of columnar-grained ice made in a laboratory

TSSN

0 7 0 1 - 5 2 3 2

DENSITY

OF

COLUMNAR-GRAINED

ICE MADE I N A LABORATORY by

Masayoshi Nakawo

-AN

A t Y

Z E D

Columnar-grained fresh-water ice, classified as 5-2 i c e (Michel and

Ramseier, 1969) i s f a i r l y easy to grow in a laboratory, simulating t h e

ice commonly found i n lakes and rivers. This laboratary-made ice has

been used intensively, t h e r e f o r e , f o r investigating t h e mechanical

properties of ice (e-g., Gold, 1 9 7 2 ; Frederking, 1977; S i n h a , 1 9 7 8 ) .

It was found necessary to determine its density w i t h reasonable accuracy

f o r f u t u r e i n v e s t i g a t i o n s , The hydrostatic method was adopted because of

i t s feasibility and wide applicability f o r various types of i c e , such a s snow i c e and sea i c e . Measurements were made w i t h t h e i c e grown by t h e

standard method described by Gold (1972). The density

of

single ice

crystal prepared by t h e zone-melting method (Ramseier, 19661, was a l s o

determined by the same procedure.

PR I N C 1

PLE OF

THE

MEASUREMENTS

Weight o f an i c e specimen C0.08 to 0.09 kg] was measured b o t h in air

[Ha) and i n i c e s a t u r a t e d 2, 2 , 4 trimethylpentane (W

1

with a calibrated

R

electronic balance (Sartorius-Werke, Type 1204 MP) which read t o

1 kg. The volume V, mass M and density p o f a specimen are given

i

where pa and pi are t h e d e n s i t y o f the

a i r and

l i q u i d , r e s p e c t i v e l y .

DERSITY OF THE AIR

Density of dry a i r p _a [dry) is given by

-3

where pa ( d r y ) is in kg n , Ta i s air temperature in O G , and pa i s

atmospheric pressure in mb. p a with a vapour pressure of p in mh is

V

g i v e n by

As it is difficult to determine pv below the f r e e z i n g p o i n t , and

p, ( C pa (e.g., py i s about 4 mb a t -S0C), pv was assumed to be zero and hence p a = p a ( d r y ) , The error in d e n s i t y estimation caused by t h i s

assumption is d i s c u s s e d later. Ta was measured using a thermocouple with

a precision of

+

0 . 5 " C . _p was measured w i t h a calibrated ordinary

a

balemeter (? 1 mb)

DENSITY

OF

THE LIOUTD

Density of 2 , 2, 4 trimethylpentane has been determined f o r a w i d e

temperature range by several i n v e s t i g a t o r s ; t h e results have been

compiled by Rossini et a1 (19531. It shows a l i n e a r i n c r e a s e with

-3

where P is

i n

kg m and T is t h e temperature of t h e liquid i n "C.

L

R

The deviation of t h e o r i g i n a l d a t a from Equation (6) i s about -3

+

0.5 kg

m

i n ;I t e m p e r a t u r e range of 0 t o -30°C (Smysh and Stoops,

1928; Timermans, 1950).

The i n f l u e n c e of i c e saturation in t h e liquid was i n v e s t i g a t e d by - 4 3

weighing an acrylic p l a s t i c CPlexigPass) block of a b o u t 10 m in b o t h

pure and i c e saturated 2 , 2, 4 trimethylpentane. Since

no

discernible d i f f e r e n c e was obsemed, Equation (6) was a d o p t e d f o r the ice-saturated

l i q u i d d e n s i t y in the calculation of ice density. Uncertainty in t h i s

assumed density was considered to be

in

t h e same order a s t h e scatter of

-

5

t h e observed d a t a for t h e pure liquid, i . e . , ? 0 . 5 kg m

.

Precise

d e n s i t y determinations o f i c e s a t u r a t e d 2, 2 , 4 t r i m e t h y l p e n t : ~ n e was madc

by Butkovich (1953) i n a temperature range of O t o -5°C and h i s d a t a fa11

into a range g i v e n by Equation (6) with t h e accuracy of i 0 . 5 kg m-"'.

T was measured w i t h a precision o f t 0 . 0 5 O ~ by a calibrated thermocouple

a

p l a c e d a t t h e same l e v e l as t h e specimen. The measurements were made a f t e r the liquid and the specimen had reached thermal equilibrium, which was checked by monitoring t h e temperature o f a dummy i c e block t h e same s i z e as t h e i c e specimen.

ACCURACY OF THE MEASUREMENTS

AND

SAMPLE CALCULATION

The p o s s i b l e absolute error was estimated u s i n g t h e general formulae

f o r calculating t h e error of a f u n c t i o n

given by

where A£ i s the error o f she function and Axl, Ax2,

.

.

.

Ax are t h e n

-

5

The e r r o r in each w e i g h i n g was considered k 1 x 10 kg. Since

W and W were o b t a i n e d by t h e difference o f t h e weight between t h e t w o

a

e

r e a d i n g s , weight of t h e container and t h e specimen minus w e i g h t of t h e container, t h e e r r o r in K _a and M was estimated by E q u a t i o n ( 8 ) t o be

- 5 R

1 1 . 4 x 10 kg.

An

example calculation o f t h e d e n s i t y and i t s possible error is shown below, in which i n p u t d a t a are

From E q u a t i o n s (43 and ( 8 ) ,

Pa (dry) = 1.3302 5 0.0028 kg m-3

T h i s e r r o r i s m a i n l y caused by t h e uncertainty i n T

.

Taking a

Pv = 0 1 3 rnb [saturation vapour pressure at -8°C i s 3 mb),

Thc e f f e c t o f neglecting t h e water vapaur in estimating t h e density of

t h e a i r i s comparatively small because o f the low saturation v a p s u r pressure below t h e freezing p o i n t . From Equations ( 6 ) and ( 8 ) ,

More t h a n 90% of t h e error i s caused by the uncertainty in t h e liquid

d e n s i t y d e t e r m i n e d by Equation (G)

.

The r e s t is a t t r i b u t e d to t h e e r r o r i n v o l v e d in t h e measurement of T With the v a l u e s of W \ Y e , oa and p L,

and u s i n g Equation (31, p . i s estimated to be 9 1 7 . 9 3 kg n d 5 . From

1

Equations (3) and ( R ) , Api i s g i v e n by

where

Inserting t h e appropriate v a l u e s , A = 0.001, B = 0.64, C = 0.04 and

D = 0 . 1 9 , r e s u l t s i n A p i = 0.67, where a l l t h e terms a r e given in kg R - ~ .

The possible a b s o l u t e e r r o r involved

i n

thc estimation o f i c e

density i s mainly attributable to the u n c e r t a i n t y in t h e value o f t h e liquid d e n s i t y . To compare t h e r e l a t i v e value of various samples a t the

-

3

same temperature w i t h t h e same method, b p Q is considered t o be 0.04 kg

m

caused by the e r r o r in t h e measurements of TL only. The possible

-3

relative error becomes 0.20 kg m

.

RESULTS

The results o b t a i n e d a r e shown in F i g , 1. Open and s o l i d circles

respectively. Each p a i n t represents t h e mean value

of

3 t a 8 measure- rncnts. The scatter of the d a t a a2 a given temperature was about

-3

+

0.37 kg m

,

which was comparable 10 t h e estimated possible relative

-

5

e r r o r ,

+

0.20 kg m

.

No

discernible difference could be found between the densities of

single-crystal and columnar-grained i c e within t h e accuracy of the

measurements. The density increased almost linearly w i t h decreasing

temperature, although t h e r e was a slight decrease in the increasing r a t e . Ice density data d e t e r m i n e d in the p a s t were a l s o plotted in Fig. 2 f o r

comparison. Bader (1964) estimated t h e density of polycrystalline i c e in

a temperature range af Q to -30°C, based on the thermal expansion

coefficient (Butkovich, 19571 and t h e density of commercial i c e at - 3 . S 0 C

(Butkovich, 19533.

His

estimation (shown by solid line in Fig. 1 )

compared favourably w i t h t h e d a t a of t h e present study.

The author would like to thank S.J. Jones o f Environment Canada for

p r o v i d i n g a single i c e crystal, and E. Penner and N . K . Sinha

of

DBR/NIlCC

f o r t h e i r encnuragement to w r i t e t h i s r e p o r t .

REFERENCES

Badar, H . 1964. Density of i c e as a f u n c t i o n o f temperature and s t r e s s .

CRREL

Special Report 6 4 .

B u t k o v i c h , T.R. 1953. Density o f single crystals o f i c e from a

temperate glacier. SIPRE Research Paper 7.

Butkovich, T.R. 1957. Linear thermal expansion of ice, SIPRE Research

Report 40.

Eisenberg, D . , and Kauzmann, W. 1969. The structure and properties o f water. Oxford U n i v e r s i t y Press.

Frederking, R. 1977. Plane-strain compressive s t r e n g t h of columnar- grained and granular-snow i c e . J. Glaciology, Vol, 18, No. 80,

Ginnings,

D.C.,

and Corruccini, R . 3 , 1947. An improved i c e calorimeter - t h e determination o f its calibration f a c t o r and the density o f i c c at D O C , J. Research, National Bureau of Standards, Vol. 3 8 , 5 8 3 - 5 9 1 ,

Geld, L . W . 1972. The process of failure of columnar-grained i c e . Philosophical Magazine, Vol. 26, No. 2 , 311-3223,

IIobbs, P.V. 1 9 7 4 . Ice physics. Clarendsn Press.

Loasdale, K. 1958. The s t r u c t u r e of i c e . Proceedings 05 Royal Society, A247, 424-434.

MicheL, R . , and Ramseier, R.O. 1969. Classification of r i v e r and lake

ice based on i t s genesis, structure and texture. Lava1 University,

Report S-15.

Rarnseler,

R.O.

1966, Zone-melting apparatus for growing i c e

rnonocrystals. Materials Research Bulletin, Vol. 2, No. 4 , 293-297. Rossini, F.D., Pitzer, K . S , , Arnett, R.L., Braun,

R.M.,

and Pimentel,

G.C.

1953. Selected values of p h y s i c a l and thermodynamic properties of hydrocarbons and r e l a t e d compounds. Carnegie Press.

Sinha, N.K. 1978. Rheology of columnar-grained ice. Experimental

Mechanics, VoI. 18, No. 12, 464-470.

Smyth,

C.P.,

and Stoops, W . N . 1928. The d i e l e c t r i c p o l a r i z a t i o n of liquids. 111. The polarization o f t h e isomers o f heptane. Journal

of t h e American Chemical S o c i e t y , Vol. 50, 1883-1890.

Timmermans,

J.

1950, Physico-chemical constants of pure o r g a n i c

SING11 CRYSTAL ITHIS STUDY1 COLUMNAR-GRAINED ICE lTHlS STUDY1

BUTKWICH 119531

LOUSDALE (15581

EI5ENBERG AND KAUZMANN (1%9I

GINNING5 AND FORRUCClNl 11947)

BADER 119WI

TEMPERATURE. " C

Figure 1

Density o f i c e i n a temperature range of O t o - 3 0 O C . Butkovichqs value

(1953) was determined by t h e hydrostatic method for s i n g l e crystals from a

glacier and f o r commercial i c e . The

data given by Lorisdale (19581, a n d

E i senberg a n d Kauzmanm (1969) were

o b t a i n e d by determining t h e unit-cell

parameters with X-ray and electron-

diffraction measurements (Hobbs, 2974)

.

G i n n i n g s and Casruccinirs v a l u e 11947)

was obtained by the Bunsen i c e

calorimeter. Badcr's estimation (1964)

was based on Butkovich's density data

(1953) and t h e t h e r m a l expansion