Post on 17-Jul-2020
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°