CHAPTER 6: CRYSTAL GROWTH & XRD Sarah Lambart

RECAP CHAP. 5 (SEE REVIEW CHAPTER)

� Crystal twinning

� Crystal defects

� Polymorphism and isomorphism

CONTENT CHAP. 6 (2 LECTURES)

� Part 1: Crystal growing - nucleation and accretion

� Part 2: Introduction to the XRD method

PART 1- CRYSTAL GROWTH: NUCLEATION AND ACCRETION

� Environments: vapor phase, fluid phase, solid phase

CRYSTAL GROWTH

Volcanic fumaroles (Kilauea)

Calcite vein Cooling lava

Reaction rim of garnet between plagioclase and

hornblende

� In order to growth a mineral form a fluid (e.g., magma, water), you need to consider two processes:

� Nucleation

� Transport

+ appropriate P-T conditions

CRYSTAL GROWTH

CRYSTAL GROWTH

� Three possible conditions for a mineral:

�  Stable

� Metastable

� Unstable

� Activation energy: energy required to transform a metastable mineral to a stable mineral

KINETICS

� Kinetics = study of reaction rates

� Depend on T, P, composition of the system

� Reactions tend to occur more quickly at higher T’s

� Different elements will diffuse at different rates, which can cause some minerals to become stable while others remain metastable

� Nucleation: the initiation of crystal growth in a fluid (magma, water, etc..)

CRYSTAL GROWTH

� Nucleation: the initiation of crystal growth in a fluid (magma, water, etc..)

CRYSTAL GROWTH

� In order for the reaction to occur, the “energy” of the mineral must be lower than the energy of the unbounded ions/atoms in the fluid ( = the mineral must be more stable than the fluid)

� Nucleation: the initiation of crystal growth in a fluid (magma, water, etc..)

CRYSTAL GROWTH

� In order for the reaction to occur, the “energy” of the mineral must be lower than the energy of the unbounded ions/atoms in the fluid ( = the mineral must be more stable than the fluid)

� The energy of nucleation can be expressed though Gibbs free energy of formation (ΔGf)

� Determining the Gibbs free energy of formation for a crystal needs to consider both the volume and surface of the precipitating crystal

CRYSTAL GROWTH

1)  Volume energy. Consider a crystal of volume V:

ΔGv = [ΔGf(crystal)-ΔGf(fluid)]V

If ΔGv <0, the crystal is at lower energy and is “stable”: it can precipitate.

� Determining the Gibbs free energy of formation for a crystal needs to consider both the volume and surface of the precipitating crystal

CRYSTAL GROWTH

2)  Surface energy (=interfacial energy). Consider a crystal of volume V:

ΔGS = γa

where γ is the surface energy per unit area, and a is the area of the crystal.

� Gibbs free energy of formation:

ΔGf = ΔGv + ΔGs

CRYSTAL GROWTH

� Consider a spherical crystal of radius r:

ΔGf = ΔGv*(4π/3)*r3 + ΔGs*πr2

NUCLEATION

r*

� r* (or rc): critical radius

� ΔG* (or ΔGc): nucleation energy

� To form crystal you must overcome the nucleation energy barrier (or add nuclei)

NUCLEATION

r*

� r* (or rc): critical radius

� ΔG* (or ΔGc): nucleation energy

ΔGf = ΔGv*(4π/3)*r3 + ΔGs*πr2

∝r3 ∝r2

NUCLEATION

r*

� r* (or rc): critical radius

� ΔG* (or ΔGc): nucleation energy

� ΔGf = ΔGv + ΔGs

� Energy required for the nucleation and the growing increase with the surface/volume ratio.

NUCLEATION � To form crystal you must overcome the nucleation energy

barrier (or add nuclei)

⇔ homogeneous vs. heterogeneous nucleation

The nucleus has to form from a pure fluid reservoir

Dust, other nuclei,… can serve as support for nucleation: requires less energy

NUCLEATION

� Supercooling

Ex.: Halite in water

NUCLEATION

� Supercooling

nucleation energy

NUCLEATION

� Supercooling

solid

Solid

+ liquid

liquid T

X

ΔT

liquidus

solidus

CRYSTAL GROWTH

� Minimize the surface energy

Fig. 5.10 in Introduction to mineralogy (Nesse)

CRYSTAL GROWTH

� Minimize the surface energy

Fig. 5.10 in Introduction to mineralogy (Nesse)

CRYSTAL GROWTH

� Minimize the surface energy

� Three types of surfaces:

� F (=flat)

� S (= Stepped)

� K (=kinked)

CRYSTAL GROWTH

� the slow growing faces will tend to dominate in the end

DENDRITIC CRYSTALS

� Crystal growth limited by transport

ZONED CRYSTALS

� Change of composition during the growth

Element maps showing Ca and Na zonation in plagioclase. source: http://serc.carleton.edu/details/images/8598.html

OSTWALD RIPENING � This thermodynamically-driven spontaneous process occurs

because larger particles are more energetically favored than smaller particles

2h 6h 24h

OSTWALD RIPENING � This thermodynamically-driven spontaneous process occurs

because larger particles are more energetically favored than smaller particles

Log(t)

Log

(m

ea

n s

ize

)

t (s)

n

PART 2: X-RAY DIFFRACTION METHOD

� X-rays: discovered in 1895 - powerful tool to "see inside" of crystals

� Determination of crystal structure and unit cell sizes

�  Identification of minerals: powder diffraction analyse = simple and inexpensive method for identifying minerals, especially fine-grained minerals

X-RAY DIFFRACTION (XRD)

� X-rays: ability to penetrate the matter depends on density (Z)

X-RAY DIFFRACTION (XRD)

� X-rays: electromagnetic radiation – λ= 0.02-100 * 10-10 m

�  λ~ atom size

X-RAY DIFFRACTION (XRD)

X-ray Vacuum Tube Cathode (W)– electron

generator Anode (Mo, Cu, Fe, Co, Cr) –

electron target, X-ray generator

X-RAY DIFFRACTION (XRD)

� Continuous spectra (white radiation)– range of X-ray wavelengths generated by the absorption (stopping) of electrons by the target

� Characteristic X-rays – particular wavelengths created by dislodgement of inner shell electrons of the target metal; x-rays generated when outer shell electrons collapse into vacant inner shells

X-RAY DIFFRACTION (XRD)

� Characteristic X-rays �  Kα peaks created by collapse from L to K

shell

� Kβ peaks created by collapse from M to K shell

BRAGG LAW nλ = 2d sinθ �  if we know λ of the X-rays going in to the crystal, and we can measure the θ of the diffracted X-rays coming out of the crystal, then we know the spacing between the atomic planes.

POWDER METHOD

� X-ray Tube: can be oriented from 0 to 90° (monochromatic rays)

� Detector: Can be oriented from 0 to 90°

� Gionometer: to orient the crystals

� X-ray intensity plot as function of the angle

� Comparison with the spectra collections: 70,000

POWDER METHOD

� Ex. Quartz nλ = 2d sinθ ⇔θ = arcsin (nλ / 2d)

λ(Cu) = 1.54Å (anode)

d - Qtz [101] = 3.342

θ = 13.32° ; 2θ = 26.64°