ORIGINAL PAPER

High-pressure neutron diffraction study on H–D isotopeeffects in brucite

Juske Horita • Antonio M. dos Santos •

Christopher A. Tulk • Bryan C. Chakoumakos •

Veniamin B. Polyakov

Received: 27 January 2010 / Accepted: 22 April 2010 / Published online: 8 May 2010

� Springer-Verlag 2010

Abstract A neutron powder diffraction study of hydro-

genated and deuterated brucite was conducted at ambient

temperature and at pressures up to 9 GPa, using a Paris–

Edinburgh high-pressure cell at the WAND instrument of

the ORNL High Flux Isotope Reactor. The two materials

were synthesized by the same method and companion

measurements of neutron diffraction were conducted under

the same conditions. Our refinement results show that the

lattice-parameters of the a axis, parallel to the sheets of

Mg–O octahedra, decrease only slightly with pressure with

no effect of H–D substitution. However, the c axis of

Mg(OD)2 is shorter and may exhibit greater compress-

ibility with pressure than that of Mg(OH)2. Consequently,

the unit-cell volume of deuterated brucite is slightly, but

systematically smaller than that of hydrogenated brucite.

When fitted to a third-order Birch–Murnaghan equation in

terms of the normalized unit-cell volume, values of the

bulk modulus for hydrogenated and deuterated brucite

(K0 = 39.0 ± 2.8 and 40.4 ± 1.3 GPa, respectively) are,

however, indistinguishable from each other within the

experimental errors. The measured effect of H–D substi-

tution on the unit-cell volume also demonstrates that bru-

cite (and other hydrous minerals) preferentially incorporate

deuterium over hydrogen under pressure, suggesting that

the distribution of hydrogen isotopes in deep-earth condi-

tions may differ significantly from that in near-surface

environments.

Keywords Brucite � High-pressure � Neutron diffraction �H–D effect � Isotope fractionation

Introduction

The mineral brucite, Mg(OH)2, belongs to the group of the

CdI2-type minerals with a simple hexagonal layered

structure. The structure is comprised of stacked sheets of

edge-sharing octahedra of magnesium hydroxide (Fig. 1).

The octahedra are composed of magnesium ions bonded to

six hydroxide ions. The hydroxide bond is directed along

the layer stacking direction and oxygen is shared with three

magnesium atoms, resulting in a neutral sheet. The sheets

are held together by weak intermolecular forces. The high-

pressure behavior of brucite and other brucite-type miner-

als with alkaline-earth and transition metals (Ca, Mn, Fe,

Co, Ni, Cd, etc.) is of great geochemical and geophysical

interest, because these brucite-type minerals serve as a

simple, yet useful analog for more complex, hydrogen-

bearing oxide and silicate minerals in the deep-earth. In

addition, the brucite ‘‘layer’’ is a fundamental building unit

in a great variety of hydrous sheet silicates, which include

micas and clays.

The structure and dynamics of brucite-type minerals

under high pressures and/or temperatures, in particular the

position of hydrogen atoms and the nature of the interlayer

bond, have been extensively investigated as a model sys-

tem for understanding hydrous minerals under compres-

sion. Brucite encompasses a wide range of bonding from

J. Horita (&)

Chemical Sciences Division, Oak Ridge National Laboratory,

Oak Ridge, TN 37831-6110, USA

e-mail: horitaj@ornl.gov

A. M. dos Santos � C. A. Tulk � B. C. Chakoumakos

Neutron Scattering Science Division, Oak Ridge National

Laboratory, Oak Ridge, TN 37831-6110, USA

V. B. Polyakov

Institute of Experimental Mineralogy,

Russian Academy of Science, Moscow, Russia

123

Phys Chem Minerals (2010) 37:741–749

DOI 10.1007/s00269-010-0372-5

the weak interlayer interaction to strong directed bonds

within the octahedral layer. A study by Desgranges et al.

(1996) of single-crystal neutron diffraction data of

Mg(OH)2 using anharmonic models suggests that a three-

site split-atom model for the H position, in which the H

atom is displaced from the three-fold axis, is the most

realistic. Parise et al. (1994) have proposed the same three-

site split-atom model to best fit neutron diffraction data for

brucite under compression. Chakoumakos et al. (1997)

used the same split-site model to fit low temperature neu-

tron diffraction data. The fact that this disorder persists to

low temperature supports the idea that the displacement of

the H atom has a large static component.

High-pressure studies, both experimental and theoreti-

cal, have revealed various other phenomena in brucite-type

hydroxides, including pressure-induced amorphization,

pressure-induced OH frequency softening, crystal structure

changes, hydrogen repulsion, and structural frustration

(Catti et al. 1995; Duffy and Ahrens 1991; Duffy et al.

1995; Hermansson et al. 2008; Kruger et al. 1989; Mook-

herjee and Stixrude 2006; Parise et al. 1994; Raugei et al.

1999; Shinoda et al. 2002). The appearance of a new

frequency and hysteresis of the original O–H stretching

frequency with pressure, detected by IR and Raman spec-

troscopy, were interpreted as a phase transition, which

involved displacements of hydrogen atoms from their ori-

ginal axial sites. Several investigators (Fei and Mao 1993;

Fukui et al. 2003; Nagai et al. 2000; Xia et al. 1998) also

reported the unit-cell volume of Mg(OH)2 up to 33 GPa at

ambient temperature, using synchrotron X-ray radiation.

Neutron diffraction techniques have also been used to

determine the unit-cell volumes and full structural data of

Mg(OH)2 (Catti et al. 1995) and Mg(OD)2 (Chakoumakos

et al. 1997; Parise et al. 1994) to 10 GPa, and Mg(OD)2

to 5 K at ambient pressure (Chakoumakos et al. 1997).

Brillouin scattering measurements at ambient pressure

highlight the anisotropy of the elastic constants (Xia et al.

1998).

A close examination of the above high-pressure dif-

fraction studies suggest that the unit-cell volume of

Mg(OD)2 appears slightly, but systematically smaller than

that of Mg(OH)2 and that the difference in the unit-cell

volumes may increase with increasing pressure to 10 GPa.

However, the experimental data of the unit-cell volumes

for Mg(OH)2 have rather large scatter, and data for

Mg(OD)2 are limited. The previous neutron diffraction

study of Mg(OD)2 under pressure (Parise et al. 1994)

suggests that the off-axis disorder of the deuterium atoms

in response to D–D repulsion is accentuated by compres-

sion, while a similar study on hydrogenated brucite (Catti

et al. 1995) finds the ordered model to be satisfactory.

These reported differences and discrepancies in the unit-

cell volume and the location of hydrogen between

Mg(OH)2 and Mg(OD)2 at high pressures have several

important implications. First, deuterated compounds are

usually used for neutron diffraction studies to avoid large

incoherent scattering from hydrogen, assuming implicitly

that hydrogenated and deuterated compounds have the

same structures, including the position of hydrogen atoms.

However, the above inspection of literature data on brucite

suggests that this assumption may not be valid under high-

pressure environments. If this is true, deuterated analogs to

hydrogenous compounds should be used with caution.

More importantly, such subtle, yet detectable differences in

the structure and atomic positions between hydrogenated

and deuterated minerals can provide insights into hydrogen

bonds and H–H repulsion under pressures. Second, H–D

isotope effects on the unit-cell volume of hydrous minerals

are directly related to the reduced partition function ratio

for hydrogen isotopes of minerals, the quantity that deter-

mines equilibrium distribution of hydrogen isotopes in

nature. Thus, accurate measurements of the differences in

the unit-cell volume of hydrogenated and deuterated bru-

cite can provide direct information on the distribution of

hydrogen isotopes in brucite and other hydrous minerals

under deep-earth conditions.

Experimental procedure

Materials

After removing fines by elutriation in water, MgO powder

(99.95% purity on metal basis, Alfa Aesar) was heated in

vacuum at 900�C for 2 days to remove traces of water.

About 10 g of the dehydrated MgO was loaded into a

Fig. 1 The structure of brucite.

Left: view down the c axis

showing the MgO layer in the

ab plane and right: the layer

stacking along the c axis

(vertical). Mg, golden;

O, red; H/D, light gray

742 Phys Chem Minerals (2010) 37:741–749

123

Teflon cup along with about 80 g of either de-ionized water

(D/H & 0.015%) or heavy water (99.9% purity, Cam-

bridge Isotope Laboratory). The Teflon cup was then

placed inside a 300 mL bolted-closure reaction vessel,

and heated to 300�C and a vapor-saturated pressure

(ca. 8.5 MPa) for 2 weeks to hydrothermally synthesize

hydrogenated or deuterated brucite by the reaction:

MgO ? H2O or D2O ? Mg(OH)2 or Mg(OD)2. Labora-

tory X-ray powder diffraction confirmed the product of

these reactions to be pure brucite with the following lattice

parameters: Mg(OH)2—a axis, 3.14786(2) A; c axis,

4.77075(1) A; unit-cell volume, 40.9400(4) A3 and

Mg(OD)2—a axis, 3.14760(2) A; c axis, 4.75525(2) A;

unit-cell volume, 40.8003(4) A3. Even after 3 years of the

synthesis of the deuterated sample, Raman spectroscopy

showed no measurable peak of OH-stretching and a Riet-

veld refinement of neutron powder diffraction pattern at

ambient condition shows [99% of deuteration.

Neutron diffraction experiment

High-pressure neutron powder diffraction measurements of

the hydrogenated and deuterated brucite were conducted at

room temperature, using a Paris–Edinburgh opposed anvil

high-pressure vessel (model VX-5) with boron nitride

anvil, which reduces scattering from the pressure cell itself.

Powdered Mg(OH)2 and Mg(OD)2 were mixed with dried

NaCl powder as a pressure calibrant in a weight ratio of

about 4:1 and pressed into pellets. These pellets were

loaded into the Paris–Edinburgh cell using a Ti–Zr (null

scattering alloy) gasket and a few drops of Fluorinert were

added as a pressure medium, which can provide a hydro-

static pressure up to a maximum of 2.3 GPa (Varga et al.

2003). The cell was pressurized manually, using an Ener-

Pac hydraulic hand-pump.

Neutron diffraction data of the brucite were acquired

with the US-Japan Wide-Angle Neutron Diffractometer

(WAND) of the High Flux Isotope Reactor at Oak Ridge

National Laboratory. The WAND is designed to provide

fast measurements of medium-resolution (intrinsic angular

resolution of 0.25�) powder-diffraction patterns, equipped

with a curved, one-dimensional 3He position-sensitive

detector covering a 125� scattering angle range from 5� to

130� with a sample to detector distance of 71 cm. The

neutron beam is monochromated by a 311 Ge crystal and

the wavelength used was 1.4785 A. For each experiment

with hydrogenated and deuterated brucite, a total of eight

measurements were conducted with increasing pressure

from 0 to approximately 9 GPa (Table 1). The acquisition

time at each pressure ranged from 2 to 6 h. The experi-

mental setup and conditions were the same for the two sets

of experiments to reduce any possible systematic differ-

ences arising from the experimental conditions. Ta

ble

1R

efin

edla

ttic

ep

aram

eter

san

du

nit

-cel

lv

olu

me

of

NaC

l,an

dh

yd

rog

enat

edan

dd

eute

rate

db

ruci

teu

nd

erp

ress

ure

Oil

pre

ssu

re(b

ar)

Mg

(OH

) 2M

g(O

D) 2

NaC

l(A

)P

ress

ure

(GP

a)a

(A)

c(A

)V

(A3)

NaC

l(A

)P

ress

ure

(GP

a)a

(A)

c(A

)V

(A3)

05

.65

64

(35

)0

.00

(4)

3.1

52

1(1

)4

.78

51

8(5

)4

1.1

75

2(2

)5

.65

39

(12

)0

.00

(1)

3.1

51

72

(3)

4.7

62

13

(2)

40

.96

64

0(7

)

15

05

.59

54

(26

)0

.84

(4)

3.1

43

1(1

)4

.72

34

3(3

)4

0.4

10

8(2

)5

.62

10

(14

)0

.44

(2)

3.1

46

88

(5)

4.7

26

66

(2)

40

.53

65

6(1

0)

30

05

.54

06

(26

)1

.73

(4)

3.1

31

3(5

)4

.66

07

5(7

)3

9.5

76

6(9

)5

.56

97

(17

)1

.20

(3)

3.1

38

57

(3)

4.6

72

19

(3)

39

.85

78

7(6

)

45

05

.47

45

(30

)2

.97

(6)

3.1

23

9(2

)4

.61

33

1(5

)3

8.9

89

4(3

)5

.50

60

(17

)2

.31

(3)

3.1

28

22

(4)

4.6

10

46

(4)

39

.07

23

2(8

)

60

05

.42

54

(28

)4

.05

(6)

3.1

13

7(2

)4

.57

64

9(6

)3

8.4

25

4(4

)5

.45

60

(14

)3

.31

(3)

3.1

22

00

(3)

4.5

68

00

(4)

38

.55

87

5(6

)

80

05

.36

92

(30

)5

.45

(8)

3.1

02

2(2

)4

.52

79

0(5

)3

7.7

36

2(4

)5

.40

29

(23

)4

.53

(6)

3.1

10

42

(9)

4.5

17

31

(7)

37

.84

84

8(1

8)

10

00

5.3

18

0(1

8)

6.9

1(5

)3

.08

96

(1)

4.4

82

44

(6)

37

.05

50

(2)

5.3

07

2(2

9)

7.1

7(9

)3

.08

81

2(5

)4

.43

52

3(6

)3

6.6

29

85

(10

)

12

00

5.2

57

2(3

8)

8.8

9(1

3)

3.0

78

7(5

)4

.45

12

5(1

1)

36

.53

82

(9)

5.2

44

9(4

8)

9.2

6(1

7)

3.0

72

06

(5)

4.4

05

56

(7)

36

.00

74

6(1

1)

Phys Chem Minerals (2010) 37:741–749 743

123

The Bragg peaks of Mg(OH)2 or Mg(OD)2 mixed with

NaCl show several well resolved lines at low angle at each

pressure (Fig. 2). The lattice parameters and unit-cell vol-

umes of NaCl mixed with brucite samples were extracted

from each diffraction pattern at a given pressure by means

of a LeBail fit of the Bragg diffraction data, using the

Fullprof software suite (Rodriguez-Carvajal 1993). Then,

the internal pressure of brucite-NaCl mixtures within the

Paris–Edinburgh cell was determined by fitting the com-

pressibility values of NaCl reported by Decker (1971) to a

third-order Birch–Murnaghan equation of state (EOS):

P ¼ 3

2K0

V0

V

� �73

� V0

V

� �53

!

� 1þ 3

4K0

0 � 4� � V0

V

� �23

�1

!" #;

K0

0 ¼oK0

oP

� �T

ð1Þ

where K0 is the zero pressure compressibility (bulk mod-

ulus) and K00 is a pressure-derivative of the compressibility

at constant temperature. The variable V0 is the zero pres-

sure unit-cell volume and V is the unit-cell volume at a

given pressure. Errors in the calculated pressures (about

±0.04 GPa at ambient pressure to ±0.17 GPa at 9 GPa)

were obtained by propagating the error in the refined lattice

parameters of NaCl (Table 1).

Results and discussion

Lattice parameters and unit-cell volume

The quality of the powder diffraction patterns for deuterated

and hydrogenated brucite is quite different owing to

the large bound incoherent scattering of hydrogen

(80.27 barns), compared with deuterium (2.05 barns)

(Fig. 2). Also, since H and D have significantly different

neutron scattering lengths (-3.74 and 6.671 fm, respec-

tively), the relative intensity of the Bragg reflections is

significantly different. For instance, the low angle (001)

reflection of brucite is much more intense in the hydroge-

nated sample facilitating the refinement of the c parameter

with neutron scattering data, but this reflection is weak in

the deuterated sample. On the other hand, the (100)

reflection is extremely weak in the hydrogenated sample,

but is present in the deuterated one. Only three reflections of

NaCl [(111), weak; (200), strong; and (220), medium) were

usable as a pressure standard throughout the pressure range,

due to the medium resolution of the powder diffractometer

(WAND), increasing background from the pressure cell

with pressure, and the overall reduction in signal as the

incident beam aperture is reduced by the gap between the

anvils closing with increasing pressure. In addition, since

NaCl is more compressible than brucite, the (200) reflection

of NaCl overlaps with the (100) reflection of brucite over

Fig. 2 Typical neutron diffraction patterns and Le Bail refinement

fits for hydrogenated (top) and deuterated brucite (bottom) at about

9 GPa. The background is much more prominent in the hydrogenated

sample due to the large incoherent scattering of H (experimental data,

blue; calculated, red/orange; difference curve, green/light blue). The

data in the range of 40–488 (2h) were not included for refinement due

to large backgrounds

744 Phys Chem Minerals (2010) 37:741–749

123

most of the pressure range. Despite these limitations, it was

still possible to extract lattice parameters of good quality for

both hydrogenated and deuterated brucite under pressure,

using at least five reflections (Table 1).

Our refined lattice parameters (a and c) with pressure are

shown in Fig. 3. It is clear that for both samples of brucite,

compressibility along the c axis is much larger than the

direction along the a axis, resulting in the rapid decrease of

the c/a ratios. This is because the weaker interlayer inter-

action is more compressible than the strong Mg oxide

bonds within the octahedral layer. This has already been

observed by many investigators (Catti et al. 1995; Duffy

et al. 1995; Fei and Mao 1993; Jayachandran and Liu 2006;

Nagai et al. 2000) and our results are consistent with these

literature data. It was noticed previously that the data of Fei

and Mao (1993) deviate systematically from those obtained

by many other investigators at pressures above 10 GPa.

Also, several investigators (Catti et al. 1995; Fei and Mao

1993; Nagai et al. 2000) observed discontinuities in the c/a

ratio around 9–12 GPa. However, our results and more

recent crystal structural (Duffy et al. 1995) and elasticity

(Xia et al. 1998) studies show no such discontinuity,

although the pressure of the discontinuity may be beyond

the pressure range of the current study. The apparent dis-

continuities in c/a are most likely due to nonhydrostatic

deviatoric stress caused by significant preferred orientation.

These deviatoric stresses on the a and c axes tend to

compensate each other, so that the unit-cell volume of

brucite decreases smoothly with pressure and the bulk of

the literature data on the unit-cell volume, including our

new data, agree reasonably well with each other.

A close examination of our results shows that the

pressure dependence of the a axis is the same, within

errors, for hydrogenated and deuterated brucite. However,

the c axis of deuterated brucite is slightly, but systemati-

cally, smaller than that of the hydrogenated sample

(Fig. 3), resulting in a more rapid decrease in the c/a ratios

of the deuterated sample compared to those of the hydro-

genated one. Accordingly, the unit-cell volume of the

deuterated brucite is somewhat smaller than that of the

hydrogenated counterpart (Fig. 4).

Recently, Sano-Furukawa et al. (2009) investigated the

compression behaviors of d-AlOOH and d-AlOOD under

quasi-hydrostatic conditions at pressures up to 63.5 and

34.9 GPa, respectively, using synchrotron X-ray diffrac-

tion. They found that at ambient pressure, the a and b axes

of d-AlOOD, which define the plane in which the hydrogen

bond lies, are longer than those of d-AOOH. As a result,

the former has greater unit-cell volumes than the latter.

However, the unit-cell volumes of d-AlOOH and d-AlOOD

become indistinguishable at high pressures ([10 GPa).

These high-pressure behaviors of d-AlOOH and d-AlOOD

observed by Sano-Furukawa et al. (2009) differ from those

observed for Mg(OH)2 and Mg(OD)2 in this study (Fig. 4).

We note that their d-AlOOD sample has only 74% of

deuterium.

Birch–Murnaghan Equation of State

The relative unit-cell volume (V/V0) of hydrogenated and

deuterated brucite obtained from our high-pressure neutron

Pressure (GPa)0 1 2 3 4 5 6 7 8 9 10

Latti

ce p

aram

eter

(an

gstr

om)

3.0

3.1

3.2

4.4

4.5

4.6

4.7

4.8

Mg(OH)2

Mg(OD)2

c-axis

a-axis

Fig. 3 Lattice parameters of hydrogenated and deuterated brucite as

a function of pressure

Pressure (GPa)0 1 2 3 4 5 6 7 8 9 10

Uni

t-ce

ll vo

lum

e (a

ngst

rom

3 )

35

36

37

38

39

40

41

42

Mg(OH)2

Mg(OD)2

Fig. 4 Refined unit-cell volume and fits to 3rd-order Birch–Murna-

ghan EOS as a function of pressure (solid lines) for hydrogenated and

deuterated brucite

Phys Chem Minerals (2010) 37:741–749 745

123

diffraction data in Table 1 were fit to the third-order Birch–

Murnaghan EOS equation (Eq. 1). The V0 values in

Table 1 were fixed, and bulk modulus (K0) and pressure-

derivative of bulk modulus (K0

0 ¼ oK0

oP ) were obtained, using

an EOS-FIT v5.2 program of Angel (2000). Although more

precise, the V0 values determined by laboratory X-ray were

not included in the dataset for the sake of data consistency.

Our values of the bulk modulus for hydrogenated and

deuterated brucite (K0 = 39.0 ± 2.8 and 40.4 ± 1.3 GPa,

respectively) are not statistically distinguishable from each

other (Table 2). Fitting with the V0 value as an adjustable

parameter yielded very similar results with slightly larger

errors (Table 2). The values obtained from this study are

consistent with the literature values, although a large range

of values (33–68.3 GPa) have been reported (Table 2).

Jiang et al. (2006) argued that some discrepancies in the

literature could be due, in part, to differences in the strain

state achieved, depending on experimental conditions and

the pressure medium used. Several previous studies (Catti

et al. 1995; Fukui et al. 2003; Nagai et al. 2000) were

conducted under non-hydrostatic conditions, which might

have caused an overestimation of the bulk modulus, due to

deviatoric stress. Our fitted values of pressure-derivative of

bulk modulus (K00) appear greater than those in the liter-

ature (Table 2), and this might be due to the effect of

possible non-hydrostatic pressure within the Paris–Edin-

burgh cell above the hydrostatic range of Fluorinert

([2.3 GPa).

The observed strong compression anisotropy of both

samples (Fig. 3) prompted us to evaluate separately the

linear modulus along the a (hard) and c (soft) axes, Ka and

Kc (Fei and Mao 1993), using the EOS-FIT v5.2 (Angel

2000):

Ka þ ma � fa ¼ P � a � c0

a0 � c

� �2=3

= fa � ð1þ fVÞ5=2� �

Kc þ mc � fc ¼ P � a0 � ca � c0

� �4=3

= fc � ð1þ fVÞ5=2� �

fa ¼1

2

a0

a

� �2

�1

� �; fc ¼

1

2

c0

c

� �2

�1

� �;

fV ¼1

2

V0

V

� �2=3

�1

" #ð2Þ

where ma and mc are adjustable parameters. The a0 and

c0 values were either fixed at the measured values or kept

Table 2 Experimental and theoretical bulk (K0) and linear (Ka and Kc) moduli, and pressure-derivative (K 0 ¼ oKoP) from this study and the

literature

V0 K0

(GPa)

Error K00 Error Ka

(GPa)

Error Kc(GPa)

Error Comment–Method Source

Experimental

41.1752 39.0 2.8 11.1 2.0 283 16 52.9 3.9 Mg(OH)2, V0 fixed in EOS-FIT This study

39.3 5.8 11.0 3.0 286 28 52.5 8.9 Same, V0 not fixed in EOS-FIT

40.9664 40.4 1.3 9.2 1.0 307 14 52.8 1.9 Mg(OD)2, V0 fixed in EOS-FIT

40.9 2.0 9.0 1.2 314 18 52.4 3.0 Same, V0 not fixed in EOS-FIT

40.878 54.3 2 4.7 0.2 388 10 75 5 Powder synchrotron X-ray Fei and Mao (1993)

47 5 4.7 Fixed Powder neutron, Mg(OD)2 Parise et al. (1994)

40.851 42 2 5.7 0.5 Single-crystal synchrotron X-ray Duffy et al. (1995)

51 4 4.6 0.4 Shock-compression Duffy and Ahrens (1991)

40.986 39 1 7.6 0.7 313 57 Powder neutron diffraction Catti et al. (1995)

36.7 Brillouin spectroscopy Xia et al. (1998)

40.8 39.6 1.4 6.7 0.7 237a 7 54.7a 2.3 Powder synchrotron X-ray Xia et al. (1998)

40.746 44 1 6.7 Fixed Powder synchrotron X-ray Nagai et al. (2000)

40.930 41.8 1.3 6.6 0.3 Powder synchrotron X-ray Fukui et al. (2003)

35.8 0.9 8.9 0.4 Brillouin spectroscopy Jiang et al. (2006)

57.1 4.7 Phase-equilibrium Saxena (1989)

Theoretical

40.86 68.3 4.0 Hartree–Fock Sherman (1991)

41.7 43 5.7 DFT(GGA) Mookherjee and Stixrude (2006)

36.7 65 6.0 DFT(LDA) Mookherjee and Stixrude (2006)

42.991 33 B3LYP Hermansson et al. (2008)

41.699 39.7 6.75 DFT(GGA) Mitev et al. (2009)

a Xia et al. (1998) equation for the linear modulus (their Eq. 2) contains errors, and their values were recalculated

746 Phys Chem Minerals (2010) 37:741–749

123

as adjustable parameters (Table 2). Please, note that

EOS-FIT v5.2 provides linear moduli Ma and Mc, and

that the relationships exist between the two types of

linear moduli: Ka = 3Ma and Kc = 3Mc. The bulk and

linear moduli for the hexagonal system satisfies the

relation: 1/K0 = 2/Ka ? 1/Kc. As expected from the data

in Fig. 3, the linear modulus of both the hydrogenated

and deuterated brucite is much greater for the a axis than

the c axis (Table 2). The values of Ka and Kc are not

readily distinguishable between hydrogenated and deu-

terated brucite (Table 2), as is the case for the bulk

modulus. However, when the c0 values are fixed at the

measured values and the pressure derivative of linear

modulus along the c axis (Kc0) is fixed at 21, a value of

Kc Mg(OD)2 (51.0 ± 0.5 GPa) is smaller than that for

Mg(OH)2 (55.3 ± 0.8 GPa).

Implications for H position under pressure

The observed compression anisotropy of brucite along the

c axis is of interest in terms of the behavior of interlayer

bonding at high-pressures. Several experimental (Parise

et al. 1994) and theoretical (Mookherjee and Stixrude

2006; Raugei et al. 1999) studies suggested that high-

pressure compression accentuates proton disorder in bru-

cite. As the octahedral layers are compressed along the c

axis, the interlayer and O…H(D) distances become shorter,

while the intralayer O–H(D) bond length stays nearly

constant or shortens only slightly (Catti et al. 1995; Parise

et al. 1994). Then, hydrogen atoms of two O–H(D) groups

from adjacent octahedral layers may start to repulse (H–H

repulsion), causing such structural changes. The neutron

diffraction study of Mg(OD)2 by Parise et al. (1994) has

shown that the hydrogen positions in brucite do not coin-

cide with the threefold symmetry axis along the c axis at

high pressures, but are split along three off-axis sites. In

another neutron diffraction study of hydrogenated brucite,

Catti et al. (1995) tested both the ordered structural model

with the H atom on the threefold axis and the disordered

model with the H atom equally distributed over three

equivalent off-axis positions. They observed that only the

ordered model converged with data collected at ambient

pressure and 7.8 GPa, and that convergence was attained

with both models for the data at the highest pressure

(10.9 GPa). In contrast, Parise et al. (1994) refined the

disordered model for their Mg(OD)2 data collected at lower

pressures (0.4–9.3 GPa). This apparent discrepancy

between two neutron diffraction studies may stem from the

fact that Parise et al. (1994) used deuterated brucite, while

Catti et al. (1995) used a hydrogenated sample, possibly

suggesting that disordering under pressure occurs much

more easily for deuterium than for hydrogen in the brucite

structure.

Our results show that the linear modulus along the c axis

(Kc) for Mg(OD)2 is smaller than that for Mg(OH)2:

51.0 ± 0.5 and 55.3 ± 0.8 GPa, respectively, when Kc0 is

fixed at 21. This in turn suggests that the c axis of deu-

terated brucite could be more compressible than that of

hydrogenated brucite at a given pressure, which might have

lead to stronger D–D than H–H repulsion. Unfortunately,

our results of linear modulus along the c axis are not

conclusive, and we were not able to further test this

hypothesis by refining the atom positions from our exper-

imental data, because the quality of our diffraction data

were somewhat compromised by overlapping peaks

between brucite and NaCl, incoherent scattering from

normal brucite, and deteriorating peak signal with pressure

(Fig. 2).

Reduced partition function ratio of brucite

under pressure

In a previous experimental study (Horita et al. 2002), we

demonstrated that the D/H fractionation factor between

brucite and water (a) increased (up to 12.4%) with

increasing pressure (up to 0.8 GPa) over the temperature

range 200–600�C:

a ¼ ðD=HÞbrucite=ðD=HÞwater ¼ bbrucite=bwater ð3Þ

where b is the D/H reduced partition function ratio. To

evaluate pressure effects on brucite itself, we have also

developed a Kieffer-type mineral model (Einstein–Debye

hybrid density of state model), using the Born–Mayer

potential function model within the quasi-harmonic

approximation. Calculated pressure effects on the b-factor

for H–D isotopes in brucite, based on our Kieffer-type

mineral model, increase linearly with pressure (ca. 15.5%in 103 lnb at 1 GPa and ambient temperature). The mag-

nitude of the pressure effects on the D/H b-factor decreases

with increasing temperature (Horita et al. 2002).

The results obtained from this study on the unit-cell

volume of hydrogenated and deuterated brucite at high-

pressure can be used to calculate directly the pressure

effects on the b-factor, using the equation:

olnboP

� �T

¼ � DV

nRTð4Þ

where DV = V* - V is the unit-cell volume isotope effect

at a given temperature and pressure. The asterisk denotes

the mineral with heavy isotopes, Mg(OD)2, and n the

number of isotopes to be exchanged within the unit cell

(n = 2 for brucite). Our results show that the unit-cell

volume of Mg(OD)2 is smaller than that of Mg(OH)2,

namely ‘‘normal’’ (DV = V* - V \ 0), and the value of

DV decreases from -0.209 A3 at ambient pressure to

-0.381 A3 at 10 GPa. Laboratory X-ray diffraction data

Phys Chem Minerals (2010) 37:741–749 747

123

gave a similar value of DV (-0.140 A3) at ambient pres-

sure. The calculations using Eq. 4 based on the Birch–

Murnaghan EOS (Table 2) show that the value of 103 lnbfor brucite increases to 322% at 10 GPa (Fig. 5). Also, we

have extended our previous calculations based on a Kief-

fer-type hybrid density of states model (Horita et al. 2002)

to 10 GPa, showing that the value of 103 lnb increases to

127 at 10 GPa (Fig. 5). Recently, Reynard and Caracas

(2009) conducted a DFT calculations on the effect of

pressure on the b-factor for D/H of brucite (Fig. 5). The

agreement among the three approaches is reasonable,

considering errors associated with the Birch–Murnaghan

EOS (Table 2).

Our data of H–D isotope effects on the unit-cell volume

of brucite at elevated pressures confirm that the b-factor of

brucite increases with pressure. This result has a direct

implication for the distribution of hydrogen isotopes in

hydrous minerals in the deep-earth. Brucite preferentially

incorporates deuterium over hydrogen with increasing

pressure. In contrast, Polyakov et al. (2006) showed that

the D/H b-factor for water decreases with pressure,

resulting in preferentially incorporation of hydrogen over

deuterium. Therefore, the D/H fractionation factor between

brucite (and other hydrous minerals) and water increases

significantly with pressure (Eq. 3), as our experimental

study of 0.8 GPa (Horita et al. 2002) demonstrated. This

pattern of deuterium enrichment in brucite continues at

least to 10 GPa, suggesting that D/H fractionation between

hydrous minerals and water under mantle conditions differ

significantly from near-surface environments. The upper

mantle contains several hydrous (OH-bearing) mineral

groups such as serpentine, chlorite, amphibole, and mica,

which are stable to depths of 200 km (ca. 7 GPa). At fur-

ther depths, various high-pressure hydrous minerals of the

system MgO–SiO2–H2O, so-called dense hydrous magne-

sium silicates (DHMS), are predicted under subducting

slab conditions of low geothermal gradients, and brucite is

a simple component of DHMS. Furthermore, it has been

suggested that considerable amounts of water, including H

and OH, are stored throughout the mantle: a third to the

same amount of the entire oceans depending on models

(Rupke et al. 2006). Thus, the isotopic behavior of

hydrogen in mantle minerals has far-reaching implications

on several important questions, including the global budget

of hydrogen isotopes and the origin of water in the earth.

Acknowledgments We thank journal reviewers (Dr. Reynard and

anonymous) for their useful comments, and Dr. Angel for his sug-

gestions in the EOS-FIT program. The WAND is operated jointly by

the Japan Atomic Energy Agency and ORNL as part of the US–Japan

Cooperative Program on Neutron Scattering. This research was

sponsored by the ORNL Laboratory Directed Research and Devel-

opment Program, and by the Division of Chemical Sciences, Geo-

sciences, and Biosciences, Office of Basic Energy Sciences, U.S.

Department of Energy under contract DE-AC05-00OR22725, Oak

Ridge National Laboratory, managed by UT-Battle, LLC.

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