Synchronizing clocks at Armageddon

Megiddo 2010

Synchronizing clocks at Armageddon

Moira Wilson School of Mechanical, Aerospace and Civil Engineering,

The University of Manchester

Megiddo 2010

RHXSome scientific observations and issues

Team RHX: Moira Wilson Chris Hall

Margaret Carter Ceren Ince

Bill Hoff

One microbalance

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Basis of method is “moisture expansion”

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Moisture induced expansion is of concern to builders and civil engineers because it gives rise to strain.

Rule of thumb: bricks should not be used for about 2 weeks after firing.(i.e. when they have finished expanding (Ha!))

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• The lime mortar accommodated strain.

• Modern cement mortars do not, so expansion joints are specified in design codes.

Moisture expansion in structural masonry

•Old brick masonry (before ~ 1950) doesnot have expansion joints.

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How big are these effects?

EXPANSION: 1 km of wall will expand by ~ 1 m over 200 y

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FILM OF BRICK GAINING MASS

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• Moisture expansion was known to be REVERSIBLE (but no agreement on the temperature required to do this)

Of most interest

• The moisture expansion was accompanied by an increase in mass (but only 1 set of data in the literature from 1962). (No point in engineering)

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The Manchester and Edinburgh worktime¼ law

(2003)

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Discovery of the (time)1/4 law:

(2003)

Megiddo 2010 (2003)

Megiddo 2010 (2003)

Fresh brick

1900 year old brick

20 year old brick

120 year old brick

Discovery of the (time)1/4 law:

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Effect of environmental conditions (i)

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Effect of environmental conditions (ii)

SATURATED

DRY

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Discovery of the 2 stage process:

0

0.1

0.2

0 2 4 6Time1/4 (mins1/4)

103 S

trai

n, ε

1 day

Expansion versus t1/4

0

0.1

0.2

0.3

0 5 10Time1/4 (min1/4)

103 ∆

m/m

o

16 days

Mass gain versus t1/4

(2005)

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TIME 1/4

The t1/4 law means that equal amounts of expansion or mass gain occur in the time intervals 1, 16, 81, 256 etcseconds / minutes/ years after firing.

These correspond to 14, 24, 34, 44 etc seconds / minutes/ years.

If we plot mass gain or expansion against t1/4 we geta straight line.

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The older the brick, the bigger it is.

Could the new rate law be exploited to produce a dating method for fired clay ceramics??

It gets bigger and heavier at a precisely defined rate

EUREKA!

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Principle of the dating method

•1 Measure initial length (L) or mass (m)

2. Measure early time mass or expansion following reheating

3. Extrapolate stage II data

4. Age of sample

t1/4

Exp

ansi

on

L,mo

L,m

ta1/4

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Expansion in fresh/reheated brick

Linear fits to Stage 2 data:(F) ε = 0.93×10-5t1/4 + 2.77×10-5

(R1) ε = 0.45×10-5t1/4 + 3.67×10-5

(R2) ε = 0.33×10-5t1/4 + 2.45×10-5

Systematic reductionin Stage II gradienton repeated reheating

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 1 2 3 4 5 6

Time1/4 (mins1/4)

10

3 Str

ain

, E

Fresh

Reheat 1

Reheat 2

1 day

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FORM of data sameas expansion data- scattery.

Same 2 stage process observed

0

0.1

0.2

0.3

0 5 10Time1/4 (min1/4)

103 ∆m

/mo

16 days

Why?

Started looking at mass gain again:

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Is the mass gain reversible?

y = 0.0039x + 0.0285

y = 0.0435x - 0.1174

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25 30

Time^0.25 /mins

Mass

gain

%

Freshly fired brick

y = 0.0039x + 0.0205

270 days y = 0.004x + 0.0248

y = 0.025x - 0.0395

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 2 4 6 8 10 12

Time^0.25 /mins

Mas

s %

gai

ned

Same brick reheated

y = 0.004x + 0.0248

7 days

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Predicted ageof 49 weeks.

5 10 15 20 25

1279.6

1280.0

1280.2

1280.4

1280.6

1279.8

1281.0

1281.4

1280.8

1281.2

1281.6

Initial mass of 39 week old brick

Extrapolated Stage II data

Stage II data

Time1/4 (min1/4)

Ma

ss (

g)

14 days

The first “dating” experiment

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m = 0.0382t 1/4 + 128.9531

m = 0.0289t 1/4 + 129.02

128

129

130

131

132

133

134

135

0 50 100 150 200

Time1/4 (mins1/4)

Mas

s (g

)

A × 1.33 = B(mean over all trials)

1,957 Years

A B

The first dating trial

Calculated date too young

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Knownage

Ratio of predicted to known age

(in t1/4)

Predicted age with average

multiplier (1.33)

(a) 150 ±10 1.36 144

(a) 150 ±10 1.31 166

(a) 150 ±10 1.26 192

(b) 367±160 1.37 298

(b) 367±160 1.37 303

(c) 1932±75 1.34 1968

(d) 1957±50 1.30 2123

Mean= 1.33

The first dating trial

All dates came outwrong-

BY THE SAME AMOUNT

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m = 0.0382t 1/4 + 128.9531

m = 0.0289t 1/4 + 129.02

128

129

130

131

132

133

134

135

0 50 100 150 200

Time1/4 (mins1/4)

Mas

s (g

)

1,957 Years

A B

The DATA

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The microbalance:

The next step…

Allows us to weigh 5 gpieces of brick under tightly controlled conditions to 0.1µg. (1/10 of a millionth of a gram).

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0

0.5

1

1.5

2

2.5

3

0 5 10Time1/4 (mins1/4)

103

∆m/m

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 2 4 6 8 10 12

Time1/4 (mins1/4)

10

3 Δm

/m0

10 days

The data

• Vastly improved quality of data.

• Speed of data acquisition.

• Absolute confirmation of the t1/4 law

NO SCATTER!!!!!!

(WHY?)

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Putting the microbalancethrough its paces

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This shows that we have a chemical reaction going on ……… and that it’s TEMPERATURE DEPENDENT!

Arrhenius plot

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EUREKA! (again)• Scattery data due to temperature fluctuationsover course of measurement period

• First dating experiment worked because the brick had been sitting in the lab for 39 weeks – and the mass gain measurements following heating were carried out at the same temp (~ 25 OC)

AND

All samples in 1st dating trial were measured at ~25 OC!

→ Stage II gradients were too steep (temp too high),

→ Extrapolated Stage II data intersected line of initial mass too soon

→ Age of sample too young (2008)

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Second dating trial

3941

3942

3943

3944

3945

3946

3947

3948

3949

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4

Time1/4 (hours1/4)

Mass

(m

g)

m /t 1/4 = -0.00006x + 0.79350

0

5

10

15

0 1000 2000 3000 4000 5000

Data points

Gra

die

nt (m

/t1/

4 )

Gradient = 0.2 min-1/4

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Started to get some REALLY good results

AND THEN …

yippee!

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We dated a Roman brick to March 2008!

(i.e. 8 months old)

AND THEN …

EEK!

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We dated a MEDIEVAL brick to 1942!

(i.e. 66 years old)

AND THEN …

– the “Canterbury Tale”…

NOW WHAT?

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Eventually…the “line of knowns”

50 person-years of effort for 6 data points!

REPLICATE VALUES (yrs)

330

321

333

308

307

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3941

3942

3943

3944

3945

3946

3947

3948

3949

0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4

Time1/4 (hours1/4)

Mass

(m

g)

m /t 1/4 = -0.00006x + 0.79350

0

5

10

15

0 1000 2000 3000 4000 5000

Data points

Gra

die

nt (m

/t1/

4 )

Improved methodology

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0.0 0.5 1.0 1.50.000

0.001

0.002

0.003

0.004

Mas

s ch

ang

e (m-m0)/m

0

Time1/4 ((hours)1/4)

Solid line: freshly-fired at 800ºC; □: following reheating at 500ºC.

1.0 1.5 2.0 2.5 3.0 3.5

0.0000

0.0005

0.0010

0.0015

0.0020(b)

Mas

s ch

ange

(m-m(2) 0)/m(2) 0

Time1/4 ((hours)1/4)

reheated

freshly-fired

(a)

Some other nice microbalance results

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NEW RESULTS:

1. Samian ware

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Samian ware Mass gain measured at 11 deg C and 30% RHfollowing reheating at 500 deg C

AGE = 1950 years

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Samian warePlot of gradient segments:

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25ºC

20ºC

15ºC

Samian wareMass gain at different temperatures:

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Samian ware

25ºC

20ºC

15ºC

11ºC

ln r = 1.6383

r = 0.1943 mg/hr1/4

Sample dates to 1943 years

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11ºC and 50 % RH

11ºC and 30 % RH

BOTH DATE TO

~ 1950 years old

Samian ware

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2. Saxon loom-weightMass gain measured at 11 deg C and 30% RH.Gradient stabilised after 7 days

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RHX age: 1159 years (= 850AD)

Assigned age:5th century8th century OR 9th century

RESULTS

Conclude 9th century

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1 2

2. Megiddo: RHX4 S7 Mass gain measured at 19 deg C and 30% RH.

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1 2

1 21

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3. Megiddo Plot of gradients vs number of data points:

The “Piasetzky Effect”

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Now have 2 sets of anomalous results:

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BET specific surface area results: SAMPLE SURFACE AREA

mm^2/g

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Thank you!

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Acknowledgements

• The Leverhulme Trust

• EPSRC

• The Museum of London Specialist Services

• Centre for Materials Science and Engineering, The University of Edinburgh

• A very patient husband (Master?)!

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Tel Aviv (hot and dry?): 32.2 OC (90 OF) and 46% RH (i.e. 46% of a large amount of water vapour)

Manchester (cold and wet) 12.8 OC (55 OF) and 67% RH (i.e. 67% of a much smaller amount of water vapour).

From these data, the water vapour pressure in Tel Aviv is 2.24 kPa compared with 1.00 kPa in Manchester

The air in Tel Aviv therefore contains much more water vapour than in Manchester