Dehydration of goethite during vacuum step-heating and implications for he retentivity characterization

Journal Pre-proof

Dehydration

goethite

during

vacuum

step-heating

and

implications for he retentivity characterization

K.A. Farley

, H.B. Monteiro, P

.M. V

asconcelos, K. W

altenber

PII:

S0009-2541(24)00334-6

DOI:

https://doi.or

g/10.1016/j.chemgeo.2024.122254

Reference:

CHEMGE 122254

To appear in:

Chemical Geology

Received date:

12 February 2024

Revised date:

4 June 2024

Accepted date:

24 June 2024

Please

cite

this

article

as:

K.A.

Farley

H.B.

Monteiro,

P.M.

Vasconcelos,

al.,

Dehydration

goethite

during

vacuum

step-heating

and

implications

for

retentivity

characterization,

Chemical

Geology

(2023),

https://doi.or

10.1016/

j.chemgeo.2024.122254

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Journal Pre-proof

Dehydration of goethite during vacuum step

heating and implications for He retentivity

characterization

K.A.

Farley

H.B.

Monteiro

Vasconcelo

, and

Waltenberg

1. Department of

eological and Planetary

Sciences

California

Institute

chnology

, Pasadena, CA

91125

USA; corresponding author

2. Earth Sciences, University of Queensland

, Brisbane, QLD 4072 Australia

Keywords: (U

Th)/He dating, goethite, hematite, He diffusion

June

, 2024

Abstract

Uncertainty exists over

what

environmental conditions and

mineralogical/chemical

properties are

required to ensure retention of

helium

such that

Th)/He dates

record the time of goethite

crystallization.

We undertook v

acuum step heating experiments to determine He diffusion paramete

for extrapolation

to Earth surface conditions on

10 goethite specimens

in which

had

created

uniform distribution of

. Arrhenius plots of

apparent

diffusion coefficients

all

samples follow the

same pattern

. At temperatures <200

C the data define arrays

consistent with

progressive

degassing of

increasingly large crystallites.

However

above 200

C the computed diffusivities increase dramatically

until about 8

of the helium is extracted, after which

they suddenly decline.

he sud

den increase in

diffusivity at 200

C coincides with the onset of

dehydration of the goethite structure

, a process which

continues through

out

the

remainder

of the step heat

There is a strong correlation between evolved

water and

He amounts.

These

observations

likely

reflect

previously reported

processes of

formation

growth

, and

coalescence of pores as the phase transition

to hematite

proceeds. While significantly

higher dehydration temperatures

of ~

270

are observed using techniques such as

ther

mogravimetric

analysis

in air

the long step

durations,

and vacuum conditions

of our experiments

destabilize goethite.

Orders of magnitude d

ifferences

in the computed diffusivities

among

our

samples

may

reflect

crystallite

size

distribution

control

dehydration kinetics

and

the

qualitative

size distributions

we infer

from the

step heat

consistent with SEM observations of crystallite

lengths

Vacuum step

heating

experiments in which goethite is decomposing cannot be used to determine He diffusion

behavior in

nature, but the inferred crystallite size distribution provide

some useful indirect evidence.

strong

relationship

exists

between

metrics of the

crystallite size distribution

from step heating

results

and

the

degree of

He retention

in nature

inferred from the

He/

He method

. This observation

provides evidence

supporting th

e validity of the

He/

technique for estimating retention, and further suggests that the

dominant control on He retention in nature is the crystallite size distributio

n. Experiments under

hydrothermal conditions in which goethite remains stable may be an alternative approach to address

the question of He diffusion behavior

in nature.

Journal Pre-proof

Introduction

Many

goethite s

pecimens have

been

analyzed using the

Th)/He

method

obtain a crystallization

age for this otherwise undatable mineral

(

e.g.,

Shuster et al., 2005; Heim et

al., 2006; Vasconcelos et al.,

2013; Danisik et al., 2013; Monteiro et al., 2014; Hofmann et al., 2017; Allard et al., 2018)

For this goal

to be realized,

helium

must either be quantitatively retained

over geologic time

, or, if

sufficiently

small

degre

es of He loss occur,

additional

data must be available from which to estimate a loss correction

(Shuster et al., 2005)

Qualitative evidence for substantial He retention under Earth surface conditions

includes reproducibility of (U

Th)/He ages

within a given goethite

specimen

or layer

(Shuster et al.,

2005; Vasconcelos et al., 2013)

, multiple ages in layered or polygenerational goethites that are either

concordant or conform to

stratigraphic constrai

nts

(Hofmann et al., 2017)

, goethite (U

Th)/He ages that

vary

systematically across the landscape at both regional

(Monteiro et al., 2018)

and local

(Heim et al.,

2006)

scales, goethite specimens that are extremely old

(Vasconcelos et al., 2013; Monteiro et al., 2020)

and concordance between

goethite (U

Th)/He ages

and cryptomelane

Ar/

Ar ages of weathering

horizon

(Vasconcelos et al., 2013)

. Each of these observations is unli

kely if goethite specimens are

poorly and variably He retentive. However, these observations provide

evidence for

the

mechanism

and

kinetics of

loss

in nature

, so

it remains unclear to what degree, and under what conditions, He

ages of goethite can be

confidently

interpreted to

reflect formation ages.

Laboratory experiments provide

alternative ways to assess He retentivity of goethite

In a first

assessment,

Shuster et al.

(

2005)

undertook

vacuum step heating

experiments on two vitreous goethite

samples

that had been irradiated to generate a uniform distribution of

He as diffusant

. Interpreted in

terms of

volume diffusion of He

, the results indicate t

he presence of at

least

two distinct diffusion

domains differing

greatly

in He retentivity under Earth surface conditions.

The domains could be

crystallites of differing sizes, regions that differ in crystallinity, or a retentivity contrast between

individ

ual crystallites and the bulk aggregate specimen.

He/

experiments

that document

the

concentration distribution

(Shuster and

Farley, 2004)

offer

completely

independent evidence for He

retentivity

. Using this method

previous workers have concluded that und

er Earth surface conditions,

analy

zed goethites retain 8

0% or more of in

itu produced radiogenic helium

(Shuster et al., 2005;

Vasconcelos et al., 2013)

. However, it is unclear how

these

result

can

be extrapo

lated to other

specimens, especially given large variations in goethite crystallite size

and crystallinity

and

hypothesized

effects of percent

level substitution of various elements (especially Al) for Fe in the goethite structure

(Bassal et al., 2022)

Similarly

it is impossible to use

this result to establish how

temperature variations

above average Earth surface conditions

might affect

helium

loss, either associated with burial or fr

diurnal or direct

solar heating of what is commonly a surficial phase.

Molecular simulations

suggest

that He

diffusion

from goethite

is strongly anisotropic, preferentially

occurring through a relatively open channel along the b

axis (typically the long axis) of the goethite

structure

(Bassal et al., 2022)

The simul

ations further show that He diffuses

rapidly in the p

erfect

goethite structure

that retention at Earth surface temperatures is impossible.

This is clearly at odds with

existing (U

Th)/He age data.

However,

the models

further

suggest that

crystallographi

c defects

and

radiation damage block these channels and

slow He loss

Substitution

of Al in the structure

also

predicted to impede

He diffusion.

Although suggestive, these simulations

are not adequate to draw

quantitative

conclusions regarding what

is r

equired in terms of mineralogical characteristics and

environmental conditions

for a goethite sample to yield a reliable formation age using the (U

Th)/He

method.

Journal Pre-proof

Step heating diffusion experiments

have been used on many minerals to

assess He retentivity

as a

function of such factors as temperature

grain

size,

chemical composition,

and radiation damage density

(Wolf et al., 1996; Reiners and Farley, 1999; Farley, 2000; Shuster and Farley, 2009; Guenthner et al.,

2013)

. S

everal known or potential complicat

ions

exist when attempting to apply this method to

goethite

. Most obviously, goethite almost always consists of aggregates of

very

tiny crystallites, typically

with prism cross

sections

smaller than



Assuming fast diffusion in intergranular space, s

p heating

of such a

n aggregate

will simultaneously interrogate a range of crystallite sizes, violating the assumption

of a single diffusion domain

assumed by

the typical

calculation

by which step heating results are

converted to diffusivities

(

e.g., the

uations of

Fechtig and Kalbitzer, 1966)

. Failure to recognize the

presence of

multiple diffusion domains

can

yield erroneous results

for

the activation energy (E

) and

frequency factor (D

) of He diffusion

(Farley, 2018)

Detailed step heats

with

temperature cycling

are

required to

characterize

the domain size distribution and the activation energy,

as has been done for

hematite

(Farley and Flowers, 2012; Farley, 2018)

, but

such experiments have only been done in a

limited way for goethite

(Shuster et al., 2005; Vasconcelos et al., 2013)

. An added complication

is that

goethite is thermodynamically unstable relative to hematite

water upon heating above Earth surface

temperature

except under unusua

l conditions

(Majzlan et al., 2003)

Thus,

during heating,

goethite

may change

physically

in association with its conversion to hematite. Phase transformation proceeds

via

inward penetration

of micropores

from crystallite surfaces

typically

along the direction of elongation.

omplete dehydration to hematite

is thought to occur by

(Goss, 1987)

Attempts to measure

He diffusion under conditions in which goethite is transforming in this manner

may

not

cha

racterize

loss relevant in nature

The

proposed importance of radiation damage or

crystal defects

(Bassal et al., 2022)

in controlling He

diffusivity adds additional complexity. If t

he measured diffusivity is to be relevant in nature, the

abundance and types of defects must remain unchanged through

out

the step heating experiment.

There

appears to be no data on defect annealing kinetics of goethite, but

temperatures required to extract

from goethite during step heating

(Shuster et al., 2005)

are within the range of temperatures at which

defect annealing

occurs in

other phases including apatite

(Farley, 2000)

and zircon

(Guenthner et al.,

2013)

The present work was undertaken to obtain and interpret step heating data that can potentially resolve

these issues. We used proton

radiated goethites to ensure a uniform distribution of diffusant (

supplemented by

measurements that can document

radiogenic helium

retentivity experienced

by the sample prior to collection.

2. Materials and

Methods

The

goethite specimens

analyzed

here

represent a range of (U

Th)/He ages,

U and Th concentration

physical habit,

crystallite dimensions,

color, and

He/

He characteristics

These characteristics are

tabulated in Table 1 and the samples described in greater

detail in the Supplementary Text.

Three

of the

samples are from

channel iron deposits in the Hammersley province of Western Australia, one from

Lynn Peak (LYNN

A1D1

;

Vasconcelos et al.

(

2013)

) and two from Yandicoogina (YAN

0201AC and YAN

0201D2

;

Heim et al.

(

2006)

)

. Sample ROY

0202C3B

comes from a several

long hand sample of

botryoidal goethite

with long fibrous

crystals

found

in a detrital deposit

in the Chinchester Range, also in

Journal Pre-proof

the Hammersley province

(Vasconcelos et al., 2013; Monteiro et al., 2020)

Sample

WIN

0601B

is a large

(6 cm)

dense

colloform goethite specimen found

in alluvium in the Flinders Ranges, South Australia

(Monteiro e

t al., 2020)

Sample

RS34

TLCM

is a

yellow goethite (suggesting small crystallite sizes)

found in the limonite horizon of the Ravensthorpe Ni

laterite deposit in Western Australia.

The final four

specimens

(CAP L2, L3, L4, and L5)

represent four

growth zones in a large (10 cm) botryoidal goethite

collected from colluvium near the

Capão

topaz mine, Minas Gerais, Brazil. This

goethite

has the oldest

Th/He) age

we know of (

range

230

280 Ma)

CAP L2, L3, and L4 are similar to each other in

age, whi

L5 is younger (Table 1).

Crystallite size and accumulated radiation damage are two parameters that could affect He diffusivity in

goethite

. We used SEM images

(Figure 1)

to estimate crystallite sizes. This proved challenging because

most of the specimen

s contain well

gned bundles of crystallites

in which the boundaries of crystallites

are difficult to discern from each other and from cracks introduced during sample preparation.

This

makes it difficult to

identify and measure

individual crystallites and to establish that a representative

population

has been

observed

Crystallite lengths were more readily

observed

than cross sections.

Where identifiable

crystallite

lengths

were measured

using ImageJ software

Most goethite

sam

ples

exhibit a wide distribution of

lengths

In some cases (e.g., Yandi

coogina

), crystallite dimensions

could

only be observed

where crystallites grew into

open spaces

within the larger sample

For

all of these

reasons

we consider the length measurements t

o be semi

quantitative.

Nevertheless

this analysis

provide

good evidence that the average crystallite length decreases in the order ROY

0202C3B>

(CAP

L5,

WIN

0601B

)> (CAP L2,

L3,

L4,

YAN

0201AC)>>

RS34

TLCM

(Table 1)

Insufficient material was

availabl

for an SEM study of YAN

0201D2

and L

YNN

A1D1

We use radiogenic He concentration as a proxy for accumulated alpha decay

exposure and therefore of

likely radiation damage

exposure

This metric provides a lower limit on the radiation dose to the extent

that He is lost by diffusion.

All

samples have

the same He concentration within one order of magnitude

(range 1.4 to 9 nmol/g)

except

RS34

TLCM

which has a much lower concentration

(0.03 nmol/g). He

concentrations decrease in the order (

WIN

0601B

, CAP L2,L3, L4) >

CAP L5 > (LYNN A1D1, ROY

0202C3B)>

RS34

TLCM

. The two YAN samples were

dated using a method which did not include

mass estimation

so their He concentrations are not kn

own.

amples were irradiated with ~ 200 MeV protons to create

a uniform distribution of

atoms/g of

spallogenic

( Shuster et al., 2004)

Although some samples undoubtedly contained natural

cosmogenic

He, the amount is orders of magnitude smaller than created artificially.

Proton irradiation

induces radiation damage to which He diffusion may respond

, as seen in apatite

(Shuster and Farley,

2009)

Using the same calculations as

Shuster and Farley

(

2009)

we conclude that t

proton radiation

dose experienced by our samples is insignificant compared to

natural alpha decay for all samples except

RS34

TLCM

Samples

consisting of one or more mg

sized chips

of each irradiated sample

were step heated in a

projector

lamp

apparatus with a temperature uncertainty of ±2

(Farley et al., 1999)

. Different heating

schedule

were employed as we assessed how best to interrogate the kinetics of helium loss.

It was

appare

nt from the outset that

obtain reasonable yields across a range of temperatures, different

samples required different schedules.

Almost all heating schedule

involved at least one

temperature

cycled segment

We included steps above the

likely

dehydratio

temperature

to assess the

consequences of th

transition to hematite. F

or some samples the maxi

mum temperature achievable

Journal Pre-proof

with

in the lamp

device (~500

C) was high enough to complete

extract He from

the sample

as shown

by repeat extractions a

t the highest

temperature

. For other samples we used a double

walled resistance

furnace

at ~1100

for the final extraction.

The s

tep heat experiments

were undertaken

over nearly two decades, so involve several different

extraction lines and mass

spectrometers. Most measurements were made following proc

edures

previously

described for hematite

(Farley and Flowers, 2012)

. Generally, after He extraction in the

projector

lamp cell (or the furnace

for some of the final

highest temp

erature

steps) the evolved

was

purified over a pair of SAES getters, cryofocused on charcoal at 14 K, released at 34 K,

and admitted into

the mass spectrom

eter (

MAP 215

Helix SFT

, or Helix MC

). In some experiments we used a liquid

trogen trap

and/

or Ti sponge getter

upstream of the SAE

S getters to

purify He of other evolved gases,

especially water

. All analyses were standardized against the same reference gas, a 2.05

synthetic

standard with a

He abundance

and

He/

He ratio

known to better than 1% from capacitance

manometry.

In all cases

He was measured on a pulse

counting electron multiplier

;

He was measured

either on the same multiplier, or, for larger beams, on a Faraday detector.

or one of the

step heat experiment

(on sample

WIN

0601B

)

a bare

metal

liquid nitrogen

finger

was

added

the heating

cell

to trap water

potentially evolved from the sample

capacitance manometer

was also

added

The

chamber was wrapped with heating tape and heated to ~50

to reduce surface

adsorption of water

This arrangement allowed us to measure the pressure of water evolved in each

step. For most steps we trapped

condensable gases during the heating step and during inlet of He

into the vacuum purification line. We

then pumped away any

remaining

non

condensable gases,

isolated the chamber from the vacuum pump, dropped the

liquid nitrogen from the trap, and allowed

the chamber to thermally equilibrate by waiting 30 minutes. We then read t

he pressure on the

manometer.

For

two

of the

step

this experiment we intentionally left the trap off during sample

heating, then trapped out the water and proceeded as described above.

The key difference between

these two approaches is that in the former

any evolved water is rapid

ly trapped, while in the latter (and

all other experiments described here) any evolved water would mostly be in the vapor phase

during the

step

e assume that the pressure obtained

in this way

is solely that of water, a reasonable assumption

given

high

asured pressures

, in the range of 0.01

1 Torr

. For comparison, if

all

the water in the mass

of goethite we analyzed in this experiment were released in a single step, we would expect a pres

sure of

a few

Torr

. We calculated

the fraction of water released in

each step i as

H20

H2O



H2O

where the

denominator is simply the sum of the pressures released in each step. We

acknowledge

the potential for

inaccuracy in this measurement arising from factors such as non

zero blanks, surface adsorption of

water, and non

ideal behavior.

Over the course of our

experiments,

e discovered that some samples yield elevated

levels

even at

oom temperature. We discuss this phenomenon below. Here we note that this

effect

complicates blank

measurements, as we ordinarily use an i

nitial room temperature step for this purpose

As an alternative,

when initial blanks were higher than the typical val

ue of 2x10

STP of

He and 3x10

STP of

He, we blank corrected using a blank measurement made after the first few steps at elevated

temperature; these blanks were

comparable

to the typical values cited above. Except in rare cases

discussed bel

ow, blank corrections were less than 2% of either isotope. Steps with high blank

corrections are highlighted in the supplement

(Table

)

. Precision on each isotope is conservatively

estimated to be better than

% for every step; no aspect of the data inte

rpretation is affected by this

level of uncertainty.

Journal Pre-proof

e used standard spherical g

eometry equations

(Fechtig and Kalbitzer, 1966)

to compute

diffusion

coefficients from step heat

yields and durations. These equations assume a single

spherical

diffusion

omain, an assumption that is

likely

violated

polycrystalline

goethite.

For this

reason,

refer to the

computed quantity as an

“

apparent diffusion coefficient

”.

Apparent diffusion coefficient

s are useful for

assessing and quantifying polycrystalline di

ffusion domain behavior (

equivalent

o m

ultiple

diffusion

domains in

feldspar

Ar/

Ar thermochronology

(Lovera et al., 1991)

)

Geometries other than a sphere

could be applied to the generally acicular goethite crystals, but previous work has shown that it makes

little difference provided the same geometric assumptions are made when obtaining diffusion

coefficients

and

when

applyi

ng them

(Meesters and Dunai, 2002)

. A similar conclusion can be drawn

regarding the possibility of anisotropic diffusivity

(Watson et al., 2010)

He/

He spectra were acquired to investigate the distribution of natural radiogenic

He in the samples

(Shuster et al., 2005). The premise of this method is that proton

generated

He is spatially uniform

wit

hin the goethites, whereas the

He distribution may be heterogeneous owing to He loss over geologic

time. Provided the step heating experiment extracts He from degassing goethite elements of increasing

radiogenic

He retentivity as the experiment proceeds,

the resulting

He/

He spectrum (bulk normalized

He/

He as a function of cumulative

He released (F

) for each step (Shuster and Farley, 2005)) can be

related to the degree of

He loss from the bulk sample in nature. Note that the degassing elements in

goethite experiment could be individual crystallites of varying size in which the smaller ones are less

retentive in nature and degas early in the step heat. Alternatively, the elements could be portions of

individual crystallites, e.g., such that the r

im is more

He depleted than the core and degasses first in the

step heat. Previously reported

He/

He spectra (Shuster et al., 2005; Vasconcelos et al., 2013) begin with

low

He/

He ratios, rising with increasing F

to a sequence of multiple steps in w

hich

He/

He is

relatively constant. This behavior is similar to a plateau in

Ar/

Ar geochronology and has the same

general interpretation: the initial steps document partial loss of

He, while the plateau indicates a

portion of the goethite with nearly invariant, possibly loss

free,

He concentration. The greater the

degree of

He loss in nature, the shallower the initial slope of the

He/

He spectrum, the higher the

value of F

whe

n the plateau is reached, and the higher the value of the bulk

normalized

He/

ratio during the plateau. A well

defined plateau can be used to correct a He age for

He loss

(Shuster and

Far

ley, 2005)

Proton irradiation produces

He/

He ratios of about 5

10. This ratio varies with target chemistry and

with time after irradiation as

He grows in from spallogenic tritium decay (Shuster et al., 2004).

yields were corrected for spallogeni

He assuming a production ratio of 5.5; this correction was <1%

except for some of the steps of

the

poor

sample

RS34

TLCM

. Spallogenic

and the tritium

intermediary have

no consequence for interpretation of

He results.

Results

As illustrat

ed in

Figure 2

, w

plot the step heat results for every sample

in a co

nsistent fashion

. In panel

we plot the usual

apparent

diffusion

coefficient

Arrhenius plot

(ln(D/a

) vs 10

/T)

also

transform

the apparent diffusion data by computing



values

(Farley, 2000, 2018)

, where



= ln(D/a

)

measured

ln(D/a

)

reference

and ln(D/a

)

reference

is the value of ln(D/a

) on a judiciously selected reference line at the

temperature at which the measur

ement was made.

Figu

re 2

A that reference line is in red.

The utility

Journal Pre-proof



values is that they

can eliminate the strong control

exerted by temperature on diffusivity

to allow

other factors to become more evident.

For example, in a polycrystalline diffusion system, a plot of



as a

function of fractional yield of He is independent of heating schedule and constrains the crystallite size

distribution

(Farley and Flowers, 2012; Farley, 2018)

. Here we use

a reference line with slope

1.72

(corresponding to an activation energy of 143 kJ/mol)

and intercept 18.7

The

se parameters

are justified

in detail

below, but f

or the moment we note that slope

72 is the approximate mean of the Arrhenius

slope obtained

on selected

retrograde

prograde cycle results

from

all

our samples.

The intercept

of the

reference line

was chosen to yield

apparent diffusion coefficient

(lnD=

39.6)

corresponding to

90%

retention

over 10 Ma

under E

arth surface conditions

(22

, 10

/T=

33.9 with T in Kelvin

)

using an

isothermal

production

diffusion model

(Wolf et al., 1998)

In other words, the reference line must pass

through the point

33.9,

39.6 on the Arrhenius plot.

The same reference line is

always

used

to provide a

fixed point of comparison among the analyzed samples

e plot



as a function of

the cumulative

fraction of

He released

(

Panel B) and as a function of step temperature (Panel C).

3.1

Apparent diffusivity

and



alues

3.1.1

WIN

0601B

We begin

escribing results from

ample WIN

0601B

because it

nicely

illustrates

several

behavioral

regimes

common to our

goethite

step heats

. We emphasize these common regimes by referring to them

as stages, described and quantitatively defined in

Table 2

Measured

characteristics of each regime for

each sample are

listed in

Table 3

The behaviors we observe are:

Initially

apparent diffusivity

increases with temperature, but the slope

of the array

in Arrhenius space

becomes

shallower

as the experiment proceeds (

concave down segment

labelled

Stage

1 in

Figure 2

The declining slope in Stage 1

also

ident as

declining



value

continuing

through

the first

(

Figure 2

The end of Stage 1 is defined to occur when



achieves its minimum value

, in this

sample the minimum value is

1.3 ln units

in the 199

C step (

Figure 2

C).

Above

199

apparent diffusivity

begins to

increa

more rapidly

with temperature

, producing a

steeper slope

and concave

up arc

in Arrhenius space

transition

to Stage 2

is most evident from a

change in slope

from negative to positive

on the



plot

(

Figure 2

B). In this sample



values

either

increase or are nearly constant up

% in

and a temperature of

317

°C

(

Figure 2

After this

point



values decline precipitously.

The

maximum



value

in Stage 2

is 1.7

ln units.

As discussed below,

increasing



values are unexpected in a system obeying simple volume diffusion of helium

3) Through the

temperature

led

sequence

that occurs

with

in Stage 2

apparent diffusivity

defines a

very linear ar

ray (r

egion l

abeled

“

cycle

”

Figure 2

)

including both retrograde and prograde steps

. T

his

sequence

consists

of 13 data points from

229 to 180

°C

and back to 238

°C

and

yields a slope of

1.765

equivalent to an activation energy of 147 kJ/mol,

and a

linear

correlation coefficient r

of 0.99

(

Table

)

Because the reference line for our



plots was selected to have a slope (

1.72) very similar to

that

measured on samples

, this portion

of the



plot

horizontal

(

Figure 2

)

4) A

striking chan

ge in beh

avior occurs at

317

°C

the start of

Stage

when

the

apparent diffusivity

sharply

declines with increasing temperature

(

Figure 2

)

. In this stage, repeat measurements at the

same temperature yield declining

apparent diffusivities

, creating a saw

tooth pattern to this portion of

the Arrhenius array. This pattern corresponds to a steady decline in



values of more than 6 ln

units and

Journal Pre-proof

extends to the end of the

experiment

We defined Stage 3 onset to occur when a



value one ln unit

lower than the maximum

during

Stage 2 is reached.

The specific choice of a 1 ln unit reduction is

somewhat

arbitrary but

seems to capture the first point when the apparent He diffusivity behavior is

clearly different from t

he increasing or nearly invariant

values

in Stage 2. Other definitions

, for

example

using

a different amount of

reduction, could

shift the onset point slightly in either direction,

but would make no difference to our interpretations.

3.1.2

YAN

0201D2 and

LYNN

A1D1

Samples YAN

0201D

and

LYNN

A1D1 are

alike

in their step

heat pattern that

we present them

together.

As is most evident on the



plots

these two samples

closely

follow the pattern of three stages

seen in WIN

0601B (Figure

and

, with

Stages 1

3 labeled

)

albeit at different absolute positions in

terms of temperature

ln(D/a2)

Stage 1,

defined

by declining



values, extends to much higher

lues of ~0.21

(YAN

0201D2) and ~0.13 (LYNN

A1D1)

compared to the value of 0.02 in WIN

0601B

The minimum



values are also much higher, 3.14 and 2.67, respectively, compared to

1.33 in

WIN

0601B.

In all three samples

the increasing



values of

tage 2 begin

around 200

°C

, and while

both

samples show the sudden drop in

apparent diffusivity

associate

d with St

age 3, it occurs

at 234

°C

in Yan

0201D2 and at 230

°C

in Lynn

A1D1 compared to 317

°C

in WIN

0601B. T

he slope of the temperature

cycle

d portion of the arrays for

both

samples

imply an activation energy of 142 kJ/mol

, very similar to

WIN

0601B.

As in

WIN

0601B, in these two samples the temperature

cycled sequence

occurs within

Stage 2

, i.e., the rising

apparent diffusivity

and



that identifies Stage 2 occurs before and continues

after the temperature cycling sequence (Figures

). This observation

underscores the fact that

temperature cycling occurs according to a predefined schedule and interrogates m

odel diffusion

behavior in whichever stage

the cycle happens to be executed

, and the stage characteristics are

unaffected by the temperature cycle.

.1.3

Cap

As shown in Figures

and documented in

Table 3

our

different layers

(L2 to L5)

of the single hand

sample

Cap

(one analyzed

twice

, with different heating schedules

distinguished by the additional

letters D1 or D2

)

behave similarly to

each other and the previously described samples



space these

5 analyses plot essentially on top of each other (

Figure 3

)

Stage 2 begins between 190 and 200

°C

after

2.4 to 5.1% of the

He has been extracted

and with m

inimum



values

averaging

0.6 (

range

0.3 to

1.28). These F

and minimum



values are intermediate between WIN

0601B (2%,

1.33) and YAN

0201D2 (21%, 3.14).

he onset

of Stage 3

in the

Cap

samples

occurs between 2

79 and 300

°C

after

% to 91% of the

He has been extracted

The Arrhenius slopes during temperature cycling range from

1.63 to

1.9 (average

1.8, equivalent to an activation energy of 149 kJ/mol,

Table 3

liquot D1

sample CAPL4 was subjected to

temperature cycling

after heating to 200

°C

while aliquot D2 wa

cycled

after heating

to 240

°C

. As a result, the cycled portion of the D1 experiment occurs coincident with the

mini

mum in



(boundary between S

tages 1 and 2) whereas it occurs well into Stage 2 in aliquot D2.

Despite this d

istinction,

the patterns for t

hese two aliquots are not notably different

the Arrhenius

and



plots

, and the Arrhenius slopes are

similar

(153 and 136 kJ/mol)

Two additional experiments were

undertaken

on sample CAP

assess

the effects of a) an extremely

different heating sche

dule, and b)

variations in the size of the goethite chips analyzed.

CAP

L4M

consisted of

~20

roughly

prismatic chips averaging 420

μm

long and 140

μm

in cross section.

CAP

L4L

Journal Pre-proof

consisted of 4

roughly

prismatic chips

veraging 1700

μm

long and 265

μm

cross section

If either the

length or the cross

section of the chips being analyzed

corresponds to

the

He diffusion length

scale a in

D/a

, we would expect

apparent

diffusivities for

CAP

L4M

to be between a factor of

4 and a factor of

higher than for

CAP

L4L.

This would correspond to

an offset

of between 1.4 and 2.8 ln units on a



plot.

In contrast

the individual

μm

size

crystallites

correspond to

the length

scale

a, then we would

expect no difference

between the two

(e.g., it will behave as a

polycrystalline

system

(Farley, 2018)

)

For

comparison the original CAP

L4 chips were

less well size

sorted but generally

intermediate in size

; the

ranged from

400

1000

μm

long and

250

400

μm

in cross

section

Acting on the hypothesis that

the onset of Stage 2 might be associated with

phase transformations

occurring at

a specific temperature

in the range 190

200

°C

(

Table 3

and

Figure 2

)

, these two aliquots

re analyz

ed on

cooler

for

longer

heating schedule

that

involved

more than 300 ho

urs and 40 steps

at 180

°C

, followed by additional isothermal steps at 200

°C

, followed by complete extraction.

As shown

in Figure

and

these two experiments produced nearly identical results

to each other

and

Stage 2 ensues even though these

aliquots were kept 10

°C

cooler than the

expected

Stage 2

onset

temperature of 190

200

°C

ese two experiments yield



plots very similar

in structure

to the other

CAP samples

(

Figure 3

)

Both the

minimum



value and

value

at the onset of Stage 2 are

nearly

identical among all CAP

samples independent of grain size and heating schedule. However, Stage 2

reaches higher



values in the cooler

for

longer experiments

; this distinction is greater for the finer

grained aliquot (CA

L4M) than the coarser grained (CAP

L4L) (

Figure 3

There is an

additional

behavior

apparently

arising

from a change in step duration

CAP

L4L and CAP

L4M that

we expected to be inconsequential

For

both

experiments, a

fter

five

180

°C

steps of 24 hours

duration (steps

; see Table

), we switched to a long sequence of 4

hour duration steps

at the

same temperature. If

He release

obeys

Fick’s law

, the duration of the step should not affect the

apparent diffusivity

. However

in both e

xperiments the change

to a shorter duration

lded a

substantial enhancement in the rate of

accumulation

from ~0.4%/hr to ~0.6%/hr

and an associated

increas

apparent diffusivity

0.5 ln units.

This occurs in steps in which very large amounts o

are being released, so inaccurate

blank correction is not a plausible explanation.

This observation

motivated the experiment in which both water and

He yield were monitored simultaneously, described

in section 3.1.6

3.1.4

YAN

0201AC and

ROY

0202C3b

These

two

samples were subjected to heating schedules with an extremely large number of steps

up to

250 in th

e case of YAN

0201AC. These more

detailed schedules explored several additional aspects of

He loss from goethite dur

ing step heating. For exampl

the initial steps

were obtained

at room

temperature and

the experiments include

multiple

prograde

retrograde sequences that span different

temperature ranges

, occurring in different stages as defined here,

and

over

different ranges of

(especially very low yield).

In the case of YAN

0201AC, t

he declining

values of Stage 1 extend to 14.6% of the cumulative

yield

and a temperature of 170

°C

(

Figure 4

Table 3

), after which

increases slightly. Stage 3 begins at 2

°C

and 7

% cu

mulative

He yield. Temperature cycled sequences were undertaken in all three stages.

Seven such cycles in Stage 1 imply a broad range of activation energies

that

generally increase as the

experiment proceeds, ranging from 107 to 132 kJ mol

(

Table 3

)

. A si

ngle lower value of 78 kJ/mol is

Journal Pre-proof

noticeably concave up and as a result has a low linear correlation coefficient compared to the other

sequences.

Four T

cycled sequences in Stag

e 2

indicate

activation ene

gies between 127 and 140 kJ/mol

(average 132 ± 6 kJ/mol), and two sequences in Stage 3 indicate much higher activation energies of 163

and 176 kJ/mol.

ultiple isothermal steps were perfo

rmed between temperature cycles in Stage 1

and each time

the

apparent diffusivity

declines

steadil

with each successive step. For exam

ple, 16 isothermal steps at 100

°C

(steps 91 to 107, F

~4%) decline

monotonically

a total of

over 1 ln unit

(

Figure 4

A,C)

contrast in several sets of isothermal steps in Stage 2, the apparent diffusivity incr

eases slightly. For

example, three sequential steps at

179

°C

(steps 211

213, F

~18.9%

Figure 4

A,C

)

gave apparent

diffusivities that increase by 0.0

ln units

between each step.

An unusual aspect of this experiment is that

38 steps were acquired at ~23

°C

at the start of the run

characterize what appeared to be an unusually high blank. While the blank on the diffusion cell was

typically < 0.1 cps

and independent of time, these steps all yielded

levels at least

a factor of a

few

higher

. In addition, the measured

levels scale with duration of the step, ranging narrowly

around an average of ~0.5 cps/hr over durations from 1 to 10 hours.

This is consistent with

occasional

observations we have made when dating g

oethites that some samples “bleed” He into the vacuum

chamber at room temperature.

Figure 5

shows results for sample ROY

0202C3b.

this experiment only

31% of the total

was

released

prior to the fusion step. In part this

distinct behavior

results fr

generally lower step

temperatures (max

imum

250

°C

)

prior to fusion

, and in part because this sample is unusually He

retentive.

High

retentivity

evident in the Arrhenius plot

(

Figure 5

by how far below the reference

line the

apparent diffusion

coefficient

s plot

and in

Figure 5

uniquely low



values

as low as

Stage 1

is much less notable than in other samples, with Stage 2 beginning at F

of just 0.0012.

Stage

2 is well developed, with



increasing to a maximum of 0.93

before the exp

eriment was terminated at

=0.31.

Compared to other samples analyzed here, ROY

020

2C3b

is shifted downward in apparent

diffusivity and



value (i.e., it is much more He retentive), and with a far smaller fraction of

extracted in Stage 1.

Five

temperature cycled sequences in Stage 1 yielded shallow slopes, with

corresponding activation energies ranging from 72 to 101 kJ/mol. Several of these sequences define

strongly concave up curvature (

Figure 5

A). Five cycles within Stage 2 are more linear an

d indicate

activation energies ranging from 130 to 142 kJ/mol.

3.1.5

TLCM

degassing pattern

this

sample

(Fig

ure

S16

)

is consistent with the others described

here but

shifted to

much

higher apparent diffusivities

and



values

For example,

the



value at the onset of

Stage 2 is 5.01 and the maximum value during Stage 2 is 5.3

, both about 1 ln unit higher than all other

samples.

Similarly,

the onset of Stage 2

190

°C

occurs at a higher value of

(27%) than all other

samples.

This sample thus appears to be less He retentive.

Stage 3 begins at

°C

and

9%,

similar to other samples.

3.1.6

WIN

0601B

In this experiment

the yield of

both

He and water

vapor

were measured for each step

(the WA suffix

indicates that wat

er was analyzed simultaneously)

. The purpose of this experiment was to

investigate

Journal Pre-proof

the unexpected effects of step duration on He yields observed in the CAP

L4M and CAP

L4L runs. We

wished t

o assess whether a) water is being evolved from goethite as the experiment proceeds, and b)

whether water vapor surrounding the sample could reduce He yield. If both are true, then the smaller

yield

from

the 24 hour steps on CAP

L4M and CAP

L4L compared to

the 4 hour steps could arise from

the accumulation of greater water

vapor

pressure in the longer

duration

steps.

We chose to undertake

this experiment on WIN

0601B given the

simple

behavior observed on the first aliquot (

Figure 2

) and

because we had a lar

ge amount of irradiated material (allowing readily measured water yields).

Each

step was held for 1 hour duration, and

sometimes

successive

steps were run at the same temperature.

No temperature cycle was undertaken.

As shown in

Figure 6

, water i

released

from the sample throughout the experiment. The yields are small

1% of the total yield) until a rapid rise occurs at about 210

°C

Successive

steps undertaken at this

temperature produced increasing water yields of 0.7% and 1.5% of the total. 7% and 13%

of the water

were extracted

in the following steps

at 220 and 230

°C

, respectively. At this point we undertook a

second step at 230

°C

but without

condensing

the water during the extraction.

The water yield dropped

to 3%. Subsequent

steps at this temperat

ure

with

water vapor

again

being trapped

returned to near the

earlier, higher yields.

A similar sequence was undertaken at 240

°C

with the same result: the water yield

was lower

when the water vapor

was

not trapped during the extraction step.

A broad p

eak

water

yield occurred at

265

280

°C

and water

vapor continued to be measured to the termination of the step

heat at 330

°C

. Note that we could not measure water yield in the final (total fusion) step

, so the total

yield we used to compute fractional

yields represents only water extracted prior to total fusion

Figure 6

shows

a strong similarity

the

release pattern

He and water. This

simi

arity

includes the

initial rise in yield at 210

°C

in which successive isothermal steps yielded higher am

ounts of

He (1.2%

and 1.8%), an initial peak in

He yield at 230

°C

, and a second

and broader peak at 265

280

°C

. For the

two steps in which

water was not trapped during the step

the

He yield is anomalously low. For

example, in three steps at 230

°C

which the middle step occurred without trapping water vapor, the

He yields were 8%, 2%, and 6%, respectively. At 240 C,

He yields for an analogous sequence were 5%,

1%, and 5%.

Thus,

the presence of water vapor reduces the

He yield, just as it does the

water yield.

Apparent diffusivity of

He during this

experiment is shown in Figure

Although the

Arrhenius plot

this experiment

appears

different from that of the original aliquot of WIN

0601B (

Figure 2

)

due to the

different heating schedule

the





plots are

in very good agreement

(

Figure 7

)

For example, S

tage 2

begins

200

°C

after extraction of 1.2% of the total He, ends at 280

°C

after 85% extraction, and

reaches a maximum



value of 1.72, very similar to the first WIN

0601B aliquot (

Table 3

The two

notable

distinctions between these experiments

are the value of



at the boundary between

tages 1

and 2 (about 1 ln unit higher in the first aliquot), and the two anomalously low values of



associated

with the

steps

in which water was not trap

ped.

An additional important observation is that

the

temperature range of substantial water release (e.g., >1.5% per step, 210

290

°C

) almost exactly

corresponds to Stage 2 of the He release.

3.2

He/

He Spectra

Figure

and S18

plot

He/

He spectra

(see

also

Table

S1)

. The

He/

He spectra are

similar in shape to

those found in previous work (Shuster et al., 2005; Vasconcelos et al., 2013): early in the step heat,

He/

He ratios are low, sometimes near zero. As F

increases, the

He/

ratio rises stea

dily,

Journal Pre-proof

eventually achieving a relatively constant value (plateau) in multiple heating steps.

However, the initial

slope of the

He/

He spectrum varies substantially among the samples. In

ROY

020

2C3

and WIN

0601B

the initial rise is extremely steep and the

plateau is achieved within the first few %

or less

of F

This

pattern has been interpreted to indicate strong retentivity of

He in nature

(Shuster

and Farley, 2005;

Shuster et al., 2005; Vasconcelos et al., 2013)

the remaining samples

the slope is

shallower

and the

onset of the plateau occurs at higher

values. For

example, in

TLCM

, the sample with the

shallowest

initial

slope,

the plateau is not reached until F

=0.3.

Such a shallow slope would typically

be interpreted to indicate 10

20%

He loss in nature

(Shuster and Farley, 2005)

There is a strong relationship between the characteristics of the initial rise in the

He/

He spectrum and

both

and



at the onset of Stage 2

(see

Table 3

)

. In

Figure 8

, the samples are presented in order of

increasing F

for S

tage 2 onset from to

p to bottom, and

tages are distinguished by different line

properties.

Stage 2 onset



values for each sample are listed on each panel.

When Stage 2 begins at low

, the

He/

He spectrum is very steep (e.g.,

ROY

0202C3B and

WIN

0601B)

suggesting strong

retention in nature

. When Stage 2 begins at a

high

value of F

the

He/

He spectrum is

shallower

(less

He retention in nature)

The same statement applies to

Stage 2 onset



values: higher

onset



values are associated with shal

lower initial

He/

He slopes.

Note that the

tage boundaries

and



values

depend only on

He apparent diffusion coefficients, while the

He/

spectra document

where

He is

sited compared to the uniformly

distributed

He.

They are independent phenomena.

At the high end of F

, s

ome samples (WIN

0601B and most of the Ca

o samples,

Figure

, S18

and

Table

) depart markedly from the

He/

He spectrum

plateau value, with

He/

He ratios

decreasing,

often to a new, lower plateau. For

example, in WIN

0601B

(

Figure 8

)

He/

ratios drop from a plateau

averaging around 1.08 to a plateau averaging 0.9 in a single step at

= 0.89.

Notably, in all cases

where there is such a shift in

He/

He after the plateau, the shift occurs within one step of the onset o

Stage 3. In other samples

the

He/

ratio

may rise after the plateau (

e.g.,

LYNN

A1D1

), but this only

ever

occurs in Stage 3. I

n still others the plateau extends to the exhaustion of

from the sa

mple (e.g.,

YAN

0201AC

Discussion

4.1

Activation

nergy

of helium release

The step heat data reported here reveal

consistent

He release

behavior among samples

that

evident

from Arrhenius plots of apparent diffusivity, but is even

better expressed

when combined with



plots

that minimize

the details of the step heating schedule (

e.g.

, Figure

B,C). For a



plot to be

most

effective it must largely elimin

ate the effects of temperature

by employing a reference line with slope

corresponding to

the activation energy of the He release process

. Thus

e begin by discussing the

activation energies implied by the temperature cycled

sequences. As shown in

Table 3

and

Figure 9

most

temperature cycles

were

undertaken in Stage 2

and

yield

highly linear Arrhenius subarrays with

slopes that are simi

r among the samples. For example

14 o

f 16 of these sequences yield

activation

energies

of 140

10 kJ/mol (range

127 to 158 kJ/mol

)

These results indica

te that the mechanism of He

evolution from goethites in Stage 2

, the stage in which most He is

released,

has

an activation

energy

close to

the value of

143 kJ/m

ol we chose for the reference line

For comparison, a

n activation energy of

140

kJ/mol

is very similar to that

He diffusion

measured on

apatite

(Wolf et al., 1996)

and

lower than

measured

zircon and

hematite

(Farley and Flowers, 2012; Guenthner et al., 2013

; Farley, 2018)

Journal Pre-proof

However

it is important to recognize that t

he existence of linear arrays on our Arrhenius plots

need not

be associated with volume diffusion of He;

linearity

simply implies that the

He release

process is

thermally activated

and the med

ium is not changing substantially

during the temperature cycle

emperature cycle

data

were obtained during Stage 1 on only two

samples

, YAN

0201AC and ROY

0202C3b. Arrhenius subarrays

in Stage 1

are less linear then in Stage

(

Table 3

)

and

indicate

lower

and

more variable activation

energies

. As shown in

Figure 9

taken together these two samples reveal a

steady increase in activation energy with F

. Values below the 140 ± 10 kJ/mol characteristic of Stage

2 are only found with

values < 1.5%.

Stage 1 temperature cycles undertaken above this value of

are consistent with the ~140 kJ/mol activation energy characteristic of Stage 2.

Activation energies

n Stage 3

were only measured on YAN

0201

AC but

are significantly

igher than in

Stage 2

63 and 176

kJ/mol;

Figure 9

). Our chosen value of 143 kJ/mol as the reference slope is thus most directly relevant to

the

He mobility

behavior in Stage 2.

4.2

Vacuum decomposition of goethite and the origin of the

step heat

stages

Every goethite reported h

ere has a



plot that first decreases

with

(Stage 1), but then increases

substantially (Stage 2)

before again falling rapidly (Stage 3)

The initial decrease in



is characteristic of a

polycrystalline diffusion system in which the smallest crystallites are the first to become depleted of He

(Farley, 2018)

he initially low activation energies

may

suggest that

at least

the

first ~1

% of the He

yield is being extracted

from materials with behavior distinct from the rest of the sample, possibly

associated with poorly crystalline

goethite

or gas release

from intercrystallite space

. Regardless of the

explanation for Stage 1, the rising



values in Stage 2 are

inconsistent with

the monotonic decrease



characteristic

polycrystalline diffusion system

(Farley, 2018)

The drop in



defining Stage 3 could

again be consistent with polycrystalline diffusion behavior, but this interpretation is not supported by

the higher activation energy

observed in this stage. This complex

He release

behavior

has

not been

reported for

other

mineral

;

something specific to goethite

and different from polycrystalline diffusion

behavior

must be occurring.

Thermal decomposition of goethite to hematite is a

likely explanation for these peculiar results.

Thermodynamic data indicate that at 1 bar

water

press

ure and

298 K

, goethite and hematite are at

equilibrium, but at higher temperatures and drier conditions hematite is the stable phase

(Majzlan et al.,

2003)

Thermogravi

metric analysis (TGA) in which goethite is heated at a const

ant rate of 1

°C

/min in air

indicates

dehydration temperatures

of about 270

°C

(

e.g.

Goss, 1987)

and our samples degassed much

of their He

well below

this temperature

owever

our experiments were done in vacuum a

nd over

much longer durations (step

durations

of hours).

The

step heat experiment in which we measured

evolved water vapor

shows that water

released over the entire temperature range interrogated in our

experiments,

and

there is a strong correspondence

between the fractions of water and He released in

each step (

Figure 6

s a working

hypothesis

propose

that

throughout o

ur experiments goethite

being converted to hematite

, and this phase transition

promotes

He release

If so, t

he He release

pattern

is intimately related to the

kinetics

and mechanism

of goethite dehydration. In support of this

hypothesis

, we note that th

e activation energy for dehydration of goethite to hematite has been

measured

to be

136

kJ/mol

(Sendova et

al., 2017)

similar to the

slope

of the

apparent

diffusivity

Arrhenius plots

during

Stage 2

(

Figure 9

)

Journal Pre-proof

TEM images

of goethite undergoing phase transformation

(

e.g.,

Goss, 1987)

show

that dehydration

begins on the surfaces of goethite crystallites, where water can be readily

extracted

from the crystal

structure. Because dehydration is associated with a substantial reduction in volume, it produces pores in

the dehydrating

crystallite

These pores penetrate deeper and deeper into the goethite crystals,

providing a route of egress for water. TEM images of a fully dehydrated goethite indicate

regularly

spaced parallel pores penetrating inward from crystallite surfaces with

pore di

meters

nd spacings

just a few

(Goss, 1987; Saito et al., 2016)

The penetration of pores into the structure has important

implications for reaction kinetics. R

ather than creating a passivating continuous reaction rind

hematite

on crystallite rims, the

lengthening

pores drive the reaction front into unreacted goethite

leaving finely twinned hematite crystallites on pore edges

(Goss, 1987; Saito et al., 2016)

Based on these obser

vations

we suggest that

at least during Stage 2

He is being

extracted

from

goethite

along with structu

ral water

, and both are then transported through the

pores

into the

surrounding vacuum chamber

ather than being controlled by He volume diffusion,

thi

s model suggests

that

He release is controlled by the kinetics and mechanism of goethite dehydration.

We propose that

nitially, in Stage 1,

temperatures are low

and

dehydration kinetics are slow enough that only a small

amount of water and He are released

(

Figure 6

)

. Whether

the small amount of

water released in Stage 1

is structural, adsorbed, or both is impossible to determine from the existing data.

Similarly,

cannot

yet determine whether He extraction

in Stage 1

is by volume diffusion or some other process.

What is

notable, however, is that Stage 1 always ends around 200

°C

At temperatures

above

200

°C

, dehydration becomes significant over the duration of our steps

, initiating

Stage 2

(

Figure 6

)

Dehydration

por

begin to extend

into the crystallites,

penetrating

unreacted

goethite

Regardless of the initial He concentration profile when this

tage begins, the pores expose

crystallite interiors with higher

e concentrations than the original crystallite

surfaces

. This enhances

the He yield, and

equally

importantly violates the assumptions used in our computation of apparent

diffusion coefficients (i.e., neither a constant domain size nor Fickian diffusive loss from that domain

pertain)

. This leads

directly

to inc

reasing



values

. Some of the best evidence for this process comes

from

successive

isothermal steps in which helium yield

increase

, for example steps 6 to 9 in CAP

L4M in

which the

individual step He

yields are 5.7%, 8.1%, 10.6% and 11.6% (Table

The

hypothesis

that dehydration regulates He

extraction

in Stage 2

is also supported by the observation

that

the He yield from WIN

0601B is greatly reduced when water vapor is not trapped on liquid nitrogen

compared with when it is trapped (Figure

, 7

). Cons

istent with Goss (1985), we interpret this

observation to indicate that the penetration of the pores into unreacted goethite is affected by how

efficiently water vapor is removed from those pores. Apparently even a tenth of a torr of water vapor is

enough

substantially

slow pore

water removal and therefore the rate of pore lengthening

and

associated He extraction.

Yapp

(1990)

mad

e similar observations regarding

the effect of evolved water

vapor pressure on the rate of

extraction of water from goethite.

The end of Stage 2 is defined by the sudden drop in



values that occurs in every sample around

=0.8

(

Table 3

)

Goss

(

1985

)

noted that after 80% transformation of goethite to hematite the

reaction rate

decreases sharply, an observation he attributed to blockage of escaping water

in the pores

and associated

abilization of

interior goethite.

According to

Naono et al.

(

1982)

his process produce

near circular voids

surrounded

ematite

possibly by coalescence

the

pores

We pro

pose

that

the

rapid reduction in He yield

associated with

tage 3 arises from this change in

goethite

behavior

Journal Pre-proof

Reduction of the rate of goethite transformation

reduce

the rate at which He

rich

interior

goe

thite is

exposed, and perhaps more importantly

He will partition into the circular voids in the neoformed

hematite.

escape, He would have to migrate through the hematite surrounding the voids.

activation energy

we measured in Stage 3

163

176

kJ/

mol is similar to observations of

He diffusion

from

pure hematite

(e.g., 157

170 kJ/mol;

(Farley and Flowers, 2012; Balout et al., 2017; Farley, 2018)

)

consistent with this interpretation

if the energetic barrier for He to enter hematite from the void is

small

our samples have about the same amount of He extracted (F

ranging from 0.

to 0.91

excluding CAP

L4M

) prior to the onset of Stage 3 despite the

enormous diversity in behavior in Stages

1 and 2 (

Table 3

)

and the range of temperatures at which this t

ransition occurred (180

300

C).

The

onset of Stage 3

the

specific

cumulative

fractional

He yield of

0.8

is likely a result of a change in

behavior as the

fraction of hematite in the sample

approaches a similar level.

4.3

Relationships among apparent diffusion characteristics and

observed goethite characteristics

In this section we relate the characteristics of the



plots to

those of

the goethite samples. All analyzed

samples yield the same general pattern in



space, but there are important distinctions

among samples

useful

metrics of these

distinctions

are th

e value

and F

t the onset of Stage 2,

and

the

maximum val

e of

uring

tage 2

(

Figure 10,

Table 3

)

. As shown in

Figure

among our sam

ples

the

tage 2

onset

values range over mo

re than 11 ln units

(factor of

60,000)

the maximum Stage 2

values

span

4 ln units

(factor of

50)

, and the fraction of

He released at the onset of

tage 2 ranges from

0.1

to 27%

(factor of 270)

The

three

metrics

are

positively correlate

(

Figure

)

We propose t

ese

relationship

arise because

all three

metrics

are indicators of the crystallite size

distribution

the goethite samples, and the He release process is dependent on

these characteristics

so,

the

large

spread in

Figure

suggests the size distributions are extremely variable within our sample

suite. We specifically suggest that when crystallites

are small

, He extraction will occur with high

apparent diffusivities (and



values)

either be

cause He volume diffusion is occurring and

the domain

size

a in D/a

small

, or because dehydration is similarly sensitive to

crystallite size (e.g., to

surface/volume ratio). If so, the samples that have high



values (e.g., R

TLCM

)

would

consist of

crystallites that tend to be smaller than in those

samples

with lower



values (e.g., ROY

0202C3b).

The

value

at the

start of Stage 2

for a specific sample likely reflect

the fraction of

crystallites

in that

sample that are small enough t

o be extracted of He by

~200

°C

(when dehydration becomes very

significant)

The value of



at th

is point

can be understood as a measure of the smallest crystallites that

still retain He when this critical temperature is achieved.

Dehydration is occurring

throughout Stage 2,

and the rate at which this occurs is reflected in the apparent He diffusivity (and

value). If dehydration

is controlled by surface/volume ratio, the maximum

value during Stage 2 for a given sample is a

measure of the largest crystal

lites in the sample.

It makes intuitive sense that samples that have smaller

crystallites

(as implied by both Δ

etrics)

also

tend to

have a higher proportion of crystallites small

enough to be extracted

of He

200

°C

, accounting for the correlations in

Figure

Factors of up to

60,000 in crystallite size are not unreasonable

if crystallite sizes range from a few unit cells

up to tens

hundreds

of micr

ometers.

As a final observation, we note that the sample that

for many hours

bled

He at room temperature in

vacuum (YAN

0201AC)

is inferred to have

amongst the smallest crystallites

using the metrics

mentioned

Journal Pre-proof

above

(

Figure

Table 3

)

. This raises the possibility that

He release from extremely tiny

crystallites

happens in real time,

likely assisted by vacuum conditions that dehydrate high surface/volume ratio

materials.

Within our sample suite this

conceptual

model suggests that crystallite sizes become larger in the order

TLCM

(

LYNN

A1D1

YAN

0201D2

YAN

0201AC

)

< CAP

<WIN

0201B <

0202C3b.

This order is in reasonable

qualitative

agreement with our SEM measurements (Table

)

in which

mean

crystallite

length increases in th

order

RS34

TLCM

YAN<CAP L1

WIN

0201B

0202C3b.

Molecular

modeling

(Bassal et al., 2022)

has suggested that radiation damage

is a key control on He

diffusion from goethite, and one might

suggest

could

play

role in our vacuum step heat experiments

as well.

In this regard we note that the He concentration variations (a proxy for radiation damage) do

not correlate well with

the metrics in Figure

lium

concentration increase

in the order:

RS34

TLCM

<< (LYNN A1D1, ROY 0202C3B) < CAP L5

< (

WIN

0601B

, CAP

L2,

L3, L4). This is very different

from the

relative

order

ing

we observe for

Δ and F

at the onset of Stage 2, and the maximum value

Δ d

uring Stage 2

Most notably, the

most extreme sample by the

step heat metrics

(

ROY

0202C3

)

has the second lowest He concentration.

If radiation damage does play a role in these experiments, it

appears to be subordinate to crystallite size distribution.

4.4

Implications

of step heat data

for He retentivity in nature

If conversion to hematite

is driving He removal from goethite in our step heat experiments,

the

apparent diffusion coefficient

and activation energies

we measured

may be of

no direct relevance to

He loss

from goethite

in nature

We believe the evidence is strong that phase decomp

osition controls He

loss behavior

in Stages 2 and 3, but it is less clear for Stage 1.

For that

reason,

we consider implications

of our results measured

early in the step heats as possible predictors of He loss in nature

Assuming

our approximate mean

activation energy of 143 kJ/mol applies

to He diffusion

in Stage 1,

and

also assuming

a polycrystalline diffusion system,

the measured



values

in Stage 1

can be used to

qualitatively assess

retentiv

ties under

arth surface conditions. As stated previou

sly, the reference line

from which



values were computed was chosen such that it

extrapolates to

a diffusivity

°C

that

would allow 90% of radiogenic He to be retained over a 10 Myr duration

. This is a reasonable if arbitrary

definition of “He retent

ive”.

ROY

0202C3b, WIN

0601B, and most of the CAP samples

yielded minimum



values below zero

with <5% of He extracted

suggesting

strong retentivity

even in the earliest

materials interrogated by the step heat

in Stage 1

However, other samples

yielded positive and

sometimes large



values

in Stage 1

. This would imply that at least the earliest degassing materials from

these samples are not very retentive

nature

. For example, if the lowest



value of 2.68 measured in

Stage 1 of YAN

0201AC app

lied to the entire sample, we would predict only 66% retention

over 10 Myr

However,

this approach ignores the fact that only the least retentive

materials (those with the smallest

crystallite sizes)

were interrogated

up to this point (i.e. in Stage 1)

; in

the case of YAN

0201AC this

constitutes just 15% of the sample.

Without knowing the

crystallite size distribution

it is impossible to

predict retentivity of the bulk sample

with this model

. Note that using the lower

Stage 1

activation

energies measured w

hen F

was <1.5% (

Figure 9

) would indicate even poorer retentivity.

We conclude that v

acuum step heat experiments provide

limited

direct

evidence bearing on the He

retentivity of goethite in nature

In particular, b

ecause

the

step heat

do not

document

e diffusi

alone

, they

cannot be used to

assess the

proposed

roles of aluminum substitution and radiation damage